Perturbative quantum gravity as a double copy of gauge theory.

PubMed

Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

2010-08-06

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

Numerical simulation of electron scattering by nanotube junctions

NASA Astrophysics Data System (ADS)

Brüning, J.; Grikurov, V. E.

2008-03-01

We demonstrate the possibility of computing the intensity of electronic transport through various junctions of three-dimensional metallic nanotubes. In particular, we observe that the magnetic field can be used to control the switch of electron in Y-type junctions. Keeping in mind the asymptotic modeling of reliable nanostructures by quantum graphs, we conjecture that the scattering matrix of the graph should be the same as the scattering matrix of its nanosize-prototype. The numerical computation of the latter gives a method for determining the "gluing" conditions at a graph. Exploring this conjecture, we show that the Kirchhoff conditions (which are commonly used on graphs) cannot be applied to model reliable junctions. This work is a natural extension of the paper [1], but it is written in a self-consistent manner.

Testing the weak gravity-cosmic censorship connection

NASA Astrophysics Data System (ADS)

Crisford, Toby; Horowitz, Gary T.; Santos, Jorge E.

2018-03-01

A surprising connection between the weak gravity conjecture and cosmic censorship has recently been proposed. In particular, it was argued that a promising class of counterexamples to cosmic censorship in four-dimensional Einstein-Maxwell-Λ theory would be removed if charged particles (with sufficient charge) were present. We test this idea and find that indeed if the weak gravity conjecture is true, one cannot violate cosmic censorship this way. Remarkably, the minimum value of charge required to preserve cosmic censorship appears to agree precisely with that proposed by the weak gravity conjecture.

Comment on ``Ratchet universality in the presence of thermal noise''

NASA Astrophysics Data System (ADS)

Quintero, Niurka R.; Alvarez-Nodarse, Renato; Cuesta, José A.

2013-12-01

A recent paper [P. J. Martínez and R. Chacón, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.87.062114 87, 062114 (2013)] presents numerical simulations on a system exhibiting directed ratchet transport of a driven overdamped Brownian particle subjected to a spatially periodic, symmetric potential. The authors claim that their simulations prove the existence of a universal waveform of the external force that optimally enhances directed transport, hence confirming the validity of a previous conjecture put forth by one of them in the limit of vanishing noise intensity. With minor corrections due to noise, the conjecture holds even in the presence of noise, according to the authors. On the basis of their results the authors claim that all previous theories, which predict a different optimal force waveform, are incorrect. In this Comment we provide sufficient numerical evidence showing that there is no such universal force waveform and that the evidence obtained by the authors otherwise is due to their particular choice of parameters. Our simulations also suggest that previous theories correctly predict the shape of the optimal waveform within their validity regime, namely, when the forcing is weak. On the contrary, the aforementioned conjecture does not hold.

Comment on "Ratchet universality in the presence of thermal noise".

PubMed

Quintero, Niurka R; Alvarez-Nodarse, Renato; Cuesta, José A

2013-12-01

A recent paper [P. J. Martínez and R. Chacón, Phys. Rev. E 87, 062114 (2013)] presents numerical simulations on a system exhibiting directed ratchet transport of a driven overdamped Brownian particle subjected to a spatially periodic, symmetric potential. The authors claim that their simulations prove the existence of a universal waveform of the external force that optimally enhances directed transport, hence confirming the validity of a previous conjecture put forth by one of them in the limit of vanishing noise intensity. With minor corrections due to noise, the conjecture holds even in the presence of noise, according to the authors. On the basis of their results the authors claim that all previous theories, which predict a different optimal force waveform, are incorrect. In this Comment we provide sufficient numerical evidence showing that there is no such universal force waveform and that the evidence obtained by the authors otherwise is due to their particular choice of parameters. Our simulations also suggest that previous theories correctly predict the shape of the optimal waveform within their validity regime, namely, when the forcing is weak. On the contrary, the aforementioned conjecture does not hold.

The General Penrose Inequality: Lessons from Numerical Evidence

NASA Astrophysics Data System (ADS)

Karkowski, J.; Malec, E.

2005-01-01

Formulation of the Penrose inequality becomes ambiguous when the past and future apparent horizons do cross. We test numerically several natural possibilities of stating the inequality in punctured and boosted single- and double-black holes, in a Dain--Friedrich class of initial data and in conformally flat spheroidal data. The Penrose inequality holds true in vacuum configurations for the outermost element amongst the set of disjoint future and past apparent horizons (as expected) and (unexpectedly) for each of the outermost past and future apparent horizons, whenever these two bifurcate from an outermost minimal surface, regardless of whether they intersect or remain disjoint. In systems with matter the conjecture breaks down only if matter does not obey the dominant energy condition.

End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture.

PubMed

Figueras, Pau; Kunesch, Markus; Tunyasuvunakool, Saran

2016-02-19

We produce the first concrete evidence that violation of the weak cosmic censorship conjecture can occur in asymptotically flat spaces of five dimensions by numerically evolving perturbed black rings. For certain thin rings, we identify a new, elastic-type instability dominating the evolution, causing the system to settle to a spherical black hole. However, for sufficiently thin rings the Gregory-Laflamme mode is dominant, and the instability unfolds similarly to that of black strings, where the horizon develops a structure of bulges connected by necks which become ever thinner over time.

Numerical operator calculus in higher dimensions

PubMed Central

Beylkin, Gregory; Mohlenkamp, Martin J.

2002-01-01

When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible. PMID:12140360

Deductive Derivation and Turing-Computerization of Semiparametric Efficient Estimation

PubMed Central

Frangakis, Constantine E.; Qian, Tianchen; Wu, Zhenke; Diaz, Ivan

2015-01-01

Summary Researchers often seek robust inference for a parameter through semiparametric estimation. Efficient semiparametric estimation currently requires theoretical derivation of the efficient influence function (EIF), which can be a challenging and time-consuming task. If this task can be computerized, it can save dramatic human effort, which can be transferred, for example, to the design of new studies. Although the EIF is, in principle, a derivative, simple numerical differentiation to calculate the EIF by a computer masks the EIF’s functional dependence on the parameter of interest. For this reason, the standard approach to obtaining the EIF relies on the theoretical construction of the space of scores under all possible parametric submodels. This process currently depends on the correctness of conjectures about these spaces, and the correct verification of such conjectures. The correct guessing of such conjectures, though successful in some problems, is a nondeductive process, i.e., is not guaranteed to succeed (e.g., is not computerizable), and the verification of conjectures is generally susceptible to mistakes. We propose a method that can deductively produce semiparametric locally efficient estimators. The proposed method is computerizable, meaning that it does not need either conjecturing, or otherwise theoretically deriving the functional form of the EIF, and is guaranteed to produce the desired estimates even for complex parameters. The method is demonstrated through an example. PMID:26237182

Deductive derivation and turing-computerization of semiparametric efficient estimation.

PubMed

Frangakis, Constantine E; Qian, Tianchen; Wu, Zhenke; Diaz, Ivan

2015-12-01

Researchers often seek robust inference for a parameter through semiparametric estimation. Efficient semiparametric estimation currently requires theoretical derivation of the efficient influence function (EIF), which can be a challenging and time-consuming task. If this task can be computerized, it can save dramatic human effort, which can be transferred, for example, to the design of new studies. Although the EIF is, in principle, a derivative, simple numerical differentiation to calculate the EIF by a computer masks the EIF's functional dependence on the parameter of interest. For this reason, the standard approach to obtaining the EIF relies on the theoretical construction of the space of scores under all possible parametric submodels. This process currently depends on the correctness of conjectures about these spaces, and the correct verification of such conjectures. The correct guessing of such conjectures, though successful in some problems, is a nondeductive process, i.e., is not guaranteed to succeed (e.g., is not computerizable), and the verification of conjectures is generally susceptible to mistakes. We propose a method that can deductively produce semiparametric locally efficient estimators. The proposed method is computerizable, meaning that it does not need either conjecturing, or otherwise theoretically deriving the functional form of the EIF, and is guaranteed to produce the desired estimates even for complex parameters. The method is demonstrated through an example. © 2015, The International Biometric Society.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Vezewski, D. J.

1980-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1979-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Computation of p -units in ray class fields of real quadratic number fields

NASA Astrophysics Data System (ADS)

Chapdelaine, Hugo

2009-12-01

Let K be a real quadratic field, let p be a prime number which is inert in K and let K_p be the completion of K at p . As part of a Ph.D. thesis, we constructed a certain p -adic invariant uin K_p^{times} , and conjectured that u is, in fact, a p -unit in a suitable narrow ray class field of K . In this paper we give numerical evidence in support of that conjecture. Our method of computation is similar to the one developed by Dasgupta and relies on partial modular symbols attached to Eisenstein series.

Joint min-max distribution and Edwards-Anderson's order parameter of the circular 1/f-noise model

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Le Doussal, Pierre

2016-05-01

We calculate the joint min-max distribution and the Edwards-Anderson's order parameter for the circular model of 1/f-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for minimum/maximum which applies to any logarithmic random energy model.

Binegativity of two qubits under noise

NASA Astrophysics Data System (ADS)

Sazim, Sk; Awasthi, Natasha

2018-07-01

Recently, it was argued that the binegativity might be a good quantifier of entanglement for two-qubit states. Like the concurrence and the negativity, the binegativity is also analytically computable quantifier for all two qubits. Based on numerical evidence, it was conjectured that it is a PPT (positive partial transposition) monotone and thus fulfills the criterion to be a good measure of entanglement. In this work, we investigate its behavior under noisy channels which indicate that the binegativity is decreasing monotonically with respect to increasing noise. We also find that the binegativity is closely connected to the negativity and has closed analytical form for arbitrary two qubits. Our study supports the conjecture that the binegativity is a monotone.

Gravity on-shell diagrams

DOE PAGES

Herrmann, Enrico; Trnka, Jaroslav

2016-11-22

Here, we study on-shell diagrams for gravity theories with any number of super-symmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only d log-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N = 8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinitymore » are present, in complete agreement with the conjecture presented in.« less

Understanding the Nature of Science and Scientific Progress: A Theory-Building Approach

ERIC Educational Resources Information Center

Chuy, Maria; Scardamalia, Marlene; Bereiter, Carl; Prinsen, Fleur; Resendes, Monica; Messina, Richard; Hunsburger, Winifred; Teplovs, Chris; Chow, Angela

2010-01-01

In 1993 Carey and Smith conjectured that the most promising way to boost students' understanding of the nature of science is a "theory-building approach to teaching about inquiry." The research reported here tested this conjecture by comparing results from two Grade 4 classrooms that differed in their emphasis on and technological…

Conjecturing, Generalizing and Justifying: Building Theory around Teacher Knowledge of Proving

ERIC Educational Resources Information Center

Lesseig, Kristin

2016-01-01

The purpose of this study was to detail teachers' proving activity and contribute to a framework of Mathematical Knowledge for Teaching Proof (MKT for Proof). While working to justify claims about sums of consecutive numbers, teachers searched for key ideas and productively used examples to make, test and refine conjectures. Analysis of teachers'…

Exploring the spectrum of planar AdS4 /CFT3 at finite coupling

NASA Astrophysics Data System (ADS)

Bombardelli, Diego; Cavaglià, Andrea; Conti, Riccardo; Tateo, Roberto

2018-04-01

The Quantum Spectral Curve (QSC) equations for planar N=6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the sl(2\\Big|1) sector. New weak coupling results for conformal dimensions of operators outside the sl(2) -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between N=6 SCS and type IIA superstring theory on AdS4 × CP 3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

Conjecture about the 2-Flavour QCD Phase Diagram

NASA Astrophysics Data System (ADS)

Nava Blanco, M. A.; Bietenholz, W.; Fernández Téllez, A.

2017-10-01

The QCD phase diagram, in particular its sector of high baryon density, is one of the most prominent outstanding mysteries within the Standard Model of particle physics. We sketch a project how to arrive at a conjecture for the case of two massless quark flavours. The pattern of spontaneous chiral symmetry breaking is isomorphic to the spontaneous magnetisation in an O(4) non-linear σ-model, which can be employed as a low-energy effective theory to study the critical behaviour. We focus on the 3d O(4) model, where the configurations are divided into topological sectors, as in QCD. A topological winding with minimal Euclidean action is denoted as a skyrmion, and the topological charge corresponds to the QCD baryon number. This effective model can be simulated on a lattice with a powerful cluster algorithm, which should allow us to identify the features of the critical temperature, as we proceed from low to high baryon density. In this sense, this projected numerical study has the potential to provide us with a conjecture about the phase diagram of QCD with two massless quark flavours.

Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chueshov, Igor, E-mail: chueshov@karazin.ua; Dowell, Earl H., E-mail: dowell@duke.edu; Lasiecka, Irena, E-mail: lasiecka@memphis.edu

2016-06-15

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelasticity, such as flutter and divergence. This leads to a partial differential equation treatment of issues such as well-posedness of finite energy solutions, and long-time (asymptotic) behavior. The latter includes theory of asymptotic stability, convergence to equilibria, and to global attracting sets. We complete the discussion with several well knownmore » observations and conjectures based on experimental/numerical studies.« less

Singularities in the classical Rayleigh-Taylor flow - Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1993-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Singularities in the classical Rayleigh-Taylor flow: Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1992-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Forming conjectures within a spreadsheet environment

NASA Astrophysics Data System (ADS)

Calder, Nigel; Brown, Tony; Hanley, Una; Darby, Susan

2006-12-01

This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus influence patterns of social interaction, and how this interaction shapes the mathematical ideas that are engaged with. Notions of conjecture, along with the particular faculty of the spreadsheet setting, are considered with regard to the facilitation of mathematical thinking. Employing an interpretive perspective, a key focus is on how alternative pedagogical media and associated discursive networks influence the way that students form and test informal conjectures.

A note on 4D heterotic string vacua, FI-terms and the swampland

NASA Astrophysics Data System (ADS)

Aldazabal, Gerardo; Ibáñez, Luis E.

2018-07-01

We present a conjecture for the massless sector of perturbative 4D N = 1 heterotic (0 , 2) string vacua, including U(1) n gauge symmetries, one of them possibly anomalous (like in standard heterotic compactifications). Mathematically it states that the positive hull generated by the charges of the massless chiral multiplets spans a sublattice of the full charge lattice. We have tested this conjecture in many heterotic N = 1 compactifications in 4D. Our motivation for this conjecture is that it allows to understand a very old puzzle in (0 , 2) N = 1 heterotic compactification with an anomalous U (1). The conjecture guarantees that there is always a D-flat direction cancelling the FI-term and restoring N = 1 SUSY in a nearby vacuum. This is something that has being verified in the past in a large number of cases, but whose origin has remained obscure for decades. We argue that the existence of a lattice generated by massless states guarantees the instability of heterotic non-BPS extremal blackholes, as required by Weak Gravity Conjecture arguments. Thus the pervasive existence of these nearby FI-cancelling vacua would be connected with WGC arguments.

Fractal dimension of spatially extended systems

NASA Astrophysics Data System (ADS)

Torcini, A.; Politi, A.; Puccioni, G. P.; D'Alessandro, G.

1991-10-01

Properties of the invariant measure are numerically investigated in 1D chains of diffusively coupled maps. The coarse-grained fractal dimension is carefully computed in various embedding spaces, observing an extremely slow convergence towards the asymptotic value. This is in contrast with previous simulations, where the analysis of an insufficient number of points led the authors to underestimate the increase of fractal dimension with increasing the dimension of the embedding space. Orthogonal decomposition is also performed confirming that the slow convergence is intrinsically related to local nonlinear properties of the invariant measure. Finally, the Kaplan-Yorke conjecture is tested for short chains, showing that, despite the noninvertibility of the dynamical system, a good agreement is found between Lyapunov dimension and information dimension.

An Early Algebra Approach to Pattern Generalisation: Actualising the Virtual through Words, Gestures and Toilet Paper

ERIC Educational Resources Information Center

Ferrara, Francesca; Sinclair, Nathalie

2016-01-01

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based…

A duality principle for the multi-block entanglement entropy of free fermion systems.

PubMed

Carrasco, J A; Finkel, F; González-López, A; Tempesta, P

2017-09-11

The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set A of sites of the subsystem considered and the set K of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets A and K to tackle complex problems by studying their dual counterparts. The duality principle is also a key ingredient in the formulation of a novel conjecture for the asymptotic behavior of the entanglement entropy of a free fermion system in the general case in which both sets A and K consist of an arbitrary number of blocks. We have verified that this conjecture reproduces the numerical results with excellent precision for all the configurations analyzed. We have also applied the conjecture to deduce several asymptotic formulas for the mutual and r-partite information generalizing the known ones for the single block case.

Revisited Fisher's equation in a new outlook: A fractional derivative approach

NASA Astrophysics Data System (ADS)

Alquran, Marwan; Al-Khaled, Kamel; Sardar, Tridip; Chattopadhyay, Joydev

2015-11-01

The well-known Fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified model is analyzed both analytically and numerically. A comparatively new technique residual power series method is used for finding approximate solutions of the modified Fisher model. A new technique combining Sinc-collocation and finite difference method is used for numerical study. The abundance of the bird species Phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters. We conjecture non-diffusive and diffusive fractional Fisher equation represents the same dynamics in the interval (memory index, α ∈(0.8384 , 0.9986)). We also observe that when the value of memory index is close to zero, the solutions bifurcate and produce a wave-like pattern. We conclude that the survivability of the species increases for long range memory index. These findings are similar to Fisher observation and act in a similar fashion that advantageous genes do.

Race, Income, and College in 25 Years: Evaluating Justice O'Connor's Conjecture. Center for Studies in Higher Education, Research & Occasional Paper Series: CSHE.19.06

ERIC Educational Resources Information Center

Krueger, Alan; Rothstein, Jesse; Turner, Sarah

2006-01-01

In Grutter v. Bollinger (2003), Justice Sandra Day O'Connor conjectured that in 25 years affirmative action in college admissions will be unnecessary. We project the test score distribution of black and white college applicants 25 years from now, focusing on the role of black-white family income gaps. Economic progress alone is unlikely to narrow…

Overlaps with arbitrary two-site states in the XXZ spin chain

NASA Astrophysics Data System (ADS)

Pozsgay, B.

2018-05-01

We present a conjectured exact formula for overlaps between the Bethe states of the spin-1/2 XXZ chain and generic two-site states. The result takes the same form as in the previously known cases: it involves the same ratio of two Gaudin-like determinants, and a product of single-particle overlap functions, which can be fixed using a combination of the quench action and quantum transfer matrix methods. Our conjecture is confirmed by numerical data from exact diagonalization. For one-site states, the formula is found to be correct even in chains with odd length. It is also pointed out that the ratio of the Gaudin-like determinants plays a crucial role in the overlap sum rule: it guarantees that in the thermodynamic limit there remains no term in the quench action.

Is it really naked? On cosmic censorship in string theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frolov, Andrei V.

We investigate the possibility of cosmic censorship violation in string theory using a characteristic double-null code, which penetrates horizons and is capable of resolving the spacetime all the way to the singularity. We perform high-resolution numerical simulations of the evolution of negative mass initial scalar field profiles, which were argued to provide a counterexample to cosmic censorship conjecture for AdS-asymptotic spacetimes in five-dimensional supergravity. In no instances formation of naked singularity is seen. Instead, numerical evidence indicates that black holes form in the collapse. Our results are consistent with earlier numerical studies, and explicitly show where the 'no black hole'more » argument breaks.« less

Broken bridges: a counter-example of the ER=EPR conjecture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Pisin; Wu, Chih-Hung; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: b02202007@ntu.edu.tw, E-mail: innocent.yeom@gmail.com

In this paper, we provide a counter-example to the ER=EPR conjecture. In an anti-de Sitter space, we construct a pair of maximally entangled but separated black holes. Due to the vacuum decay of the anti-de Sitter background toward a deeper vacuum, these two parts can be trapped by bubbles. If these bubbles are reasonably large, then within the scrambling time, there should appear an Einstein-Rosen bridge between the two black holes. Now by tracing more details on the bubble dynamics, one can identify parameters such that one of the two bubbles either monotonically shrinks or expands. Because of the changemore » of vacuum energy, one side of the black hole would evaporate completely. Due to the shrinking of the apparent horizon, a signal of one side of the Einstein-Rosen bridge can be viewed from the opposite side. We analytically and numerically demonstrate that within a reasonable semi-classical parameter regime, such process can happen. Bubbles are a non-perturbative effect, which is the crucial reason that allows the transmission of information between the two black holes through the Einstein-Rosen bridge, even though the probability is highly suppressed. Therefore, the ER=EPR conjecture cannot be generic in its present form and its validity maybe restricted.« less

Distillability of Werner states using entanglement witnesses and robust semidefinite programs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vianna, Reinaldo O.; Departamento de Fisica, ICEX, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31270-901 Belo Horizonte, Minas Gerais; Doherty, Andrew C.

2006-11-15

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.

Phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle

NASA Astrophysics Data System (ADS)

Okuyama, Kazumi

2018-04-01

We study the phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle using the exact partition function at finite N . By evaluating the exact partition function numerically, we find evidence for the existence of a series of phase transitions at non-zero θ-angle as conjectured in [hep-th/0509004

Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patommel, Jens; Klare, Susanne; Hoppe, Robert

In response to the conjecture that the numerical aperture of x-ray optics is fundamentally limited by the critical angle of total reflection, the concept of adiabatically focusing refractive lenses was proposed to overcome this limit. Here, we present an experimental realization of these optics made of silicon and demonstrate that they indeed focus 20 keV x rays to a 18.4 nm focus with a numerical aperture of 1.73(9) × 10 –3 that clearly exceeds the critical angle of total reflection of 1.55 mrad.

Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses

DOE PAGES

Patommel, Jens; Klare, Susanne; Hoppe, Robert; ...

2017-03-06

In response to the conjecture that the numerical aperture of x-ray optics is fundamentally limited by the critical angle of total reflection, the concept of adiabatically focusing refractive lenses was proposed to overcome this limit. Here, we present an experimental realization of these optics made of silicon and demonstrate that they indeed focus 20 keV x rays to a 18.4 nm focus with a numerical aperture of 1.73(9) × 10 –3 that clearly exceeds the critical angle of total reflection of 1.55 mrad.

Moments of zeta functions associated to hyperelliptic curves over finite fields

PubMed Central

Rubinstein, Michael O.; Wu, Kaiyu

2015-01-01

Let q be an odd prime power, and denote the set of square-free monic polynomials D(x)∈Fq[x] of degree d. Katz and Sarnak showed that the moments, over , of the zeta functions associated to the curves y2=D(x), evaluated at the central point, tend, as , to the moments of characteristic polynomials, evaluated at the central point, of matrices in USp(2⌊(d−1)/2⌋). Using techniques that were originally developed for studying moments of L-functions over number fields, Andrade and Keating conjectured an asymptotic formula for the moments for q fixed and . We provide theoretical and numerical evidence in favour of their conjecture. In some cases, we are able to work out exact formulae for the moments and use these to precisely determine the size of the remainder term in the predicted moments. PMID:25802418

Entanglement of purification: from spin chains to holography

NASA Astrophysics Data System (ADS)

Nguyen, Phuc; Devakul, Trithep; Halbasch, Matthew G.; Zaletel, Michael P.; Swingle, Brian

2018-01-01

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

Invariance of separability probability over reduced states in 4 × 4 bipartite systems

NASA Astrophysics Data System (ADS)

Lovas, Attila; Andai, Attila

2017-07-01

The geometric separability probability of composite quantum systems has been extensively studied in the recent decades. One of the simplest but strikingly difficult problem is to compute the separability probability of qubit-qubit and rebit-rebit quantum states with respect to the Hilbert-Schmidt measure. A lot of numerical simulations confirm the P{rebit - rebit}=\\frac{29}{64} and P{qubit-qubit}=\\frac{8}{33} conjectured probabilities. We provide a rigorous proof for the separability probability in the real case and we give explicit integral formulas for the complex and quaternionic case. Milz and Strunz studied the separability probability with respect to given subsystems. They conjectured that the separability probability of qubit-qubit (and qubit-qutrit) states of the form of ≤ft(\\begin{array}{@{}cc@{}} D1 & C \\ C* & D2 \\end{array}\\right) depends on D=D1+D2 (on single qubit subsystems), moreover it depends only on the Bloch radii (r) of D and it is constant in r. Using the Peres-Horodecki criterion for separability we give a mathematical proof for the \\frac{29}{64} probability and we present an integral formula for the complex case which hopefully will help to prove the \\frac{8}{33} probability, too. We prove Milz and Strunz’s conjecture for rebit-rebit and qubit-qubit states. The case, when the state space is endowed with the volume form generated by the operator monotone function f(x)=\\sqrt{x} is also studied in detail. We show that even in this setting Milz and Strunz’s conjecture holds true and we give an integral formula for separability probability according to this measure.

Statistics of pressure fluctuations in decaying isotropic turbulence.

PubMed

Kalelkar, Chirag

2006-04-01

We present results from a systematic direct-numerical simulation study of pressure fluctuations in an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid. At cascade completion, isosurfaces of low pressure are found to be organized as slender filaments, whereas the predominant isostructures appear sheetlike. We exhibit several results, including plots of probability distributions of the spatial pressure difference, the pressure-gradient norm, and the eigenvalues of the pressure-Hessian tensor. Plots of the temporal evolution of the mean pressure-gradient norm, and the mean eigenvalues of the pressure-Hessian tensor are also exhibited. We find the statistically preferred orientations between the eigenvectors of the pressure-Hessian tensor, the pressure gradient, the eigenvectors of the strain-rate tensor, the vorticity, and the velocity. Statistical properties of the nonlocal part of the pressure-Hessian tensor are also exhibited. We present numerical tests (in the viscous case) of some conjectures of Ohkitani [Phys. Fluids A 5, 2570 (1993)] and Ohkitani and Kishiba [Phys. Fluids 7, 411 (1995)] concerning the pressure-Hessian and the strain-rate tensors, for the unforced, incompressible, three-dimensional Euler equations.

On the use of pulsed Dielectric Barrier Discharges to control the gas-phase composition of atmospheric pressure air plasmas

NASA Astrophysics Data System (ADS)

Barni, R.; Biganzoli, I.; Dell'Orto, E.; Riccardi, C.

2014-11-01

We presents results obtained from the numerical simulation of the gas-phase chemical kinetics in atmospheric pressure air non-equilibrium plasmas. In particular we have addressed the effect of pulsed operation mode of a plane dielectric barrier discharge. It was conjectured that the large difference in the time scales involved in the fast dissociation of oxygen molecules in plasma and their subsequent reactions to produce ozone and nitrogen oxides, makes the presence of a continuously repeated plasma production unnecessary and a waste of electrical power and thus efficiency. In order to test such suggestion we have performed a numerical study of the composition and the temporal evolution of the gas-phase of atmospheric pressure air non-equilibrium plasmas. Comparison with experimental findings in a dielectric barrier discharge with an electrode configuration symmetrical and almost ideally plane is briefly addressed too, using plasma diagnostics to extract the properties of the single micro-discharges and a sensor to measure the concentration of ozone produced by the plasma.

Comments on real tachyon vacuum solution without square roots

NASA Astrophysics Data System (ADS)

Arroyo, E. Aldo

2018-01-01

We analyze the consistency of a recently proposed real tachyon vacuum solution without square roots in open bosonic string field theory. We show that the equation of motion contracted with the solution itself is satisfied. Additionally, by expanding the solution in the basis of the curly ℒ0 and the traditional L 0 eigenstates, we evaluate numerically the vacuum energy and obtain a result in agreement with Sen's conjecture.

Dirac and Klein-Gordon-Fock equations in Grumiller’s spacetime

NASA Astrophysics Data System (ADS)

Al-Badawi, A.; Sakalli, I.

We study the Dirac and the chargeless Klein-Gordon-Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.

Pair correlation and twin primes revisited.

PubMed

Conrey, Brian; Keating, Jonathan P

2016-10-01

We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe.

Pair correlation and twin primes revisited

NASA Astrophysics Data System (ADS)

Conrey, Brian; Keating, Jonathan P.

2016-10-01

We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe.

Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics

NASA Technical Reports Server (NTRS)

Fyfe, D.; Joyce, G.; Montgomery, D.

1977-01-01

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing, a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wavenumbers simultaneously with a cascade of mean square vector potential to lower wavenumbers, leading to an omni-directional magnetic energy spectrum.

Modified hoop conjecture in expanding spacetimes and primordial black hole production in FRW universe

NASA Astrophysics Data System (ADS)

Saini, Anshul; Stojkovic, Dejan

2018-05-01

According to a variant of the hoop conjecture, if we localize two particles within the Schwarzschild radius corresponding to their center of mass energy, then a black hole will form. Despite a large body of work on the formation of primordial black holes, so far this conjecture has not been generalized to expanding spacetimes. We derive a formula which gives the distance within which two particles must be localized to give a black hole, and which crucially depends on the expansion rate of the background space. In the limit of a very slow expansion, we recover the flat spacetime case. In the opposite limit of the large expansion rate when the inverse Hubble radius is smaller than the Schwarzschild radius of a "would be" black hole, the new critical distance between two particles that can make a black hole becomes equal to the particle horizon, which is just a requirement that the particles are in a causal contact. This behavior also nicely illustrates why the Big Bang singularity is not a black hole. We then use our formula to calculate the number density, energy density and production rate of black holes produced in collisions of particles. We find that though black holes might be numerous at high temperatures, they never dominate over the background radiation below the Planck temperature.

Direct Numerical Simulation of Turbulent Couette-Poiseuille Flow With Zero Skin Friction

NASA Technical Reports Server (NTRS)

Coleman, Gary N.; Spalart, Philippe R.

2015-01-01

The near-wall scaling of mean velocity U(yw) is addressed for the case of zero skin friction on one wall of a fully turbulent channel flow. The present DNS results can be added to the evidence in support of the conjecture that U is proportional to the square root of yw in the region just above the wall at which the mean shear dU=dy = 0.

Developing Learning Theory by Refining Conjectures Embodied in Educational Designs

ERIC Educational Resources Information Center

Sandoval, William A.

2004-01-01

Designed learning environments embody conjectures about learning and instruction, and the empirical study of learning environments allows such conjectures to be refined over time. The construct of embodied conjecture is introduced as a way to demonstrate the theoretical nature of learning environment design and to frame methodological issues in…

A proof of the conjecture on the twin primes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuo-ling, Zhou

2016-06-08

In this short note, we have proved the conjecture on twin primes using some thoughts of the set theory. Firstly, using the original sieve method and a new notation(concept)introduced by myself, the conjecture on twin primes is summed up as an elementary successive limit, afterwards we form a subsequence of positive integers,and using it,we prove that the successive limits are commutative and complete the proof of the conjecture on twin primes We also give a more straightforward proof of the conjecture.

The Schrödinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics

NASA Astrophysics Data System (ADS)

Briscese, Fabio

2017-09-01

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schrödinger-Poisson equations in the large N limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as \\hbar ˜ M^{5/3} G^{1/2} (N/< ρ > )^{1/6}, where is G the gravitational constant, N and M are the number and the mass of the bodies, and < ρ > is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schrödinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.

Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games.

PubMed

Duong, Manh Hong; Han, The Anh

2016-12-01

In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, [Formula: see text], and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as [Formula: see text] as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained.

On the Strong Direct Summand Conjecture

ERIC Educational Resources Information Center

McCullough, Jason

2009-01-01

In this thesis, our aim is the study the Vanishing of Maps of Tor Conjecture of Hochster and Huneke. We mainly focus on an equivalent characterization called the Strong Direct Summand Conjecture, due to N. Ranganathan. Our results are separated into three chapters. In Chapter 3, we prove special cases of the Strong Direct Summand Conjecture in…

Threshold Phenomenon for the Quintic Wave Equation in Three Dimensions

NASA Astrophysics Data System (ADS)

Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm

2014-04-01

For the critical focusing wave equation in the radial case, we establish the role of the "center stable" manifold constructed in Krieger and Schlag (Am J Math 129(3):843-913, 2007) near the ground state ( W, 0) as a threshold between blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizoń et al. (Nonlinearity 17(6):2187-2201, 2004). The underlying topology is stronger than the energy norm.

The covariant entropy conjecture and concordance cosmological models

NASA Astrophysics Data System (ADS)

He, Song; Zhang, Hongbao

2008-10-01

Recently a covariant entropy conjecture has been proposed for dynamical horizons. We apply this conjecture to concordance cosmological models, namely, those cosmological models filled with perfect fluids, in the presence of a positive cosmological constant. As a result, we find that this conjecture has a severe constraint power. Not only does this conjecture rule out those cosmological models disfavored by the anthropic principle, but also it imposes an upper bound 10-60 on the cosmological constant for our own universe, which thus provides an alternative macroscopic perspective for understanding the long-standing cosmological constant problem.

Carving out the end of the world or (superconformal bootstrap in six dimensions)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Chi-Ming; Lin, Ying-Hsuan

We bootstrap N=(1,0) superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. By assuming E 8 flavor group, we present universal bounds on the central charge C T and the flavor central charge C J. Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on C J , and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS 7×S 4/Z 2 .

Carving out the end of the world or (superconformal bootstrap in six dimensions)

DOE PAGES

Chang, Chi-Ming; Lin, Ying-Hsuan

2017-08-29

We bootstrap N=(1,0) superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. By assuming E 8 flavor group, we present universal bounds on the central charge C T and the flavor central charge C J. Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on C J , and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS 7×S 4/Z 2 .

Axion monodromy and the weak gravity conjecture

NASA Astrophysics Data System (ADS)

Hebecker, Arthur; Rompineve, Fabrizio; Westphal, Alexander

2016-04-01

Axions with broken discrete shift symmetry (axion monodromy) have recently played a central role both in the discussion of inflation and the `relaxion' approach to the hierarchy problem. We suggest a very minimalist way to constrain such models by the weak gravity conjecture for domain walls: while the electric side of the conjecture is always satisfied if the cosine-oscillations of the axion potential are sufficiently small, the magnetic side imposes a cutoff, Λ3 ˜ mf M pl, independent of the height of these `wiggles'. We compare our approach with the recent related proposal by Ibanez, Montero, Uranga and Valenzuela. We also discuss the non-trivial question which version, if any, of the weak gravity conjecture for domain walls should hold. In particular, we show that string compactifications with branes of different dimensions wrapped on different cycles lead to a `geometric weak gravity conjecture' relating volumes of cycles, norms of corresponding forms and the volume of the compact space. Imposing this `geometric conjecture', e.g. on the basis of the more widely accepted weak gravity conjecture for particles, provides at least some support for the (electric and magnetic) conjecture for domain walls.

Spectral relationships between kicked Harper and on-resonance double kicked rotor operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lawton, Wayne; Mouritzen, Anders S.; Wang Jiao

2009-03-15

Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking resemblance between the spectra of these operators. In this paper we apply C*-algebra methods to explain this resemblance. We show that each pair of corresponding operators belongs to a common rotation C*-algebra B{sub {alpha}}, prove that their spectra are equal if {alpha} is irrational, and prove that the Hausdorff distance between their spectra converges to zero as q increases if {alpha}=p/q with p and q coprime integers. Moreover, we show that corresponding operators in B{sub {alpha}}more » are homomorphic images of mother operators in the universal rotation C*-algebra A{sub {alpha}} that are unitarily equivalent and hence have identical spectra. These results extend analogous results for almost Mathieu operators. We also utilize the C*-algebraic framework to develop efficient algorithms to compute the spectra of these mother operators for rational {alpha} and present preliminary numerical results that support the conjecture that their spectra are Cantor sets if {alpha} is irrational. This conjecture for almost Mathieu operators, called the ten Martini problem, was recently proven after intensive efforts over several decades. This proof for the almost Mathieu operators utilized transfer matrix methods, which do not exist for the kicked operators. We outline a strategy, based on a special property of loop groups of semisimple Lie groups, to prove this conjecture for the kicked operators.« less

Phase ordering in disordered and inhomogeneous systems

NASA Astrophysics Data System (ADS)

Corberi, Federico; Zannetti, Marco; Lippiello, Eugenio; Burioni, Raffaella; Vezzani, Alessandro

2015-06-01

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth laws of the ordered domain size, namely logarithmic or power law, respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature that governs the presence or the absence of a finite-temperature phase transition.

Short-scale turbulent fluctuations driven by the electron-temperature gradient in the national spherical torus experiment.

PubMed

Mazzucato, E; Smith, D R; Bell, R E; Kaye, S M; Hosea, J C; LeBlanc, B P; Wilson, J R; Ryan, P M; Domier, C W; Luhmann, N C; Yuh, H; Lee, W; Park, H

2008-08-15

Measurements with coherent scattering of electromagnetic waves in plasmas of the National Spherical Torus Experiment indicate the existence of turbulent fluctuations in the range of wave numbers k perpendicular rho(e)=0.1-0.4, corresponding to a turbulence scale length nearly equal to the collisionless skin depth. Experimental observations and agreement with numerical results from a linear gyrokinetic stability code support the conjecture that the observed turbulence is driven by the electron-temperature gradient.

Rankings of International Achievement Test Performance and Economic Strength: Correlation or Conjecture?

ERIC Educational Resources Information Center

Tienken, Christopher H.

2008-01-01

Examining a popular political notion, this article presents results from a series of Spearman Rho calculations conducted to investigate relationships between countries' rankings on international tests of mathematics and science and future economic competitiveness as measured by the 2006 World Economic Forum's Growth Competitiveness Index (GCI).…

Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives

NASA Astrophysics Data System (ADS)

Bernardara, M.; Tabuada, G.

2016-06-01

Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when \\dim (S)≤ 1), Grothendieck's standard conjecture of Lefschetz type (when \\dim (S)≤ 2), and Hodge's conjecture (when \\dim(S)≤ 3).

Global conjecturing process in pattern generalization problem

NASA Astrophysics Data System (ADS)

Sutarto; Nusantara, Toto; Subanji; Dwi Hastuti, Intan; Dafik

2018-04-01

The aim of this global conjecturing process based on the theory of APOS. The subjects used in study were 15 of 8th grade students of Junior High School. The data were collected using Pattern Generalization Problem (PGP) and interviews. After students had already completed PGP; moreover, they were interviewed using students work-based to understand the conjecturing process. These interviews were video taped. The result of study reveals that the global conjecturing process occurs at the phase of action in which subjects build a conjecture by observing and counting the number of squares completely without distinguishing between black or white squares, finaly at the phase of process, the object and scheme were perfectly performed.

On the degree conjecture for separability of multipartite quantum states

NASA Astrophysics Data System (ADS)

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-01

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matrices match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.

Asymptotic safety of quantum gravity beyond Ricci scalars

NASA Astrophysics Data System (ADS)

Falls, Kevin; King, Callum R.; Litim, Daniel F.; Nikolakopoulos, Kostas; Rahmede, Christoph

2018-04-01

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from f (R ) -type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

A non-Hermitian analysis of strongly correlated quantum systems

NASA Astrophysics Data System (ADS)

Nakamura, Yuichi; Hatano, Naomichi

2006-03-01

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. Hatano and Nelson[1] applied this technique to non-interacting random electron systems. They related a non-Hermitian critical point to the inverse localization length of the Hermitian systems. We here conjecture that we can obtain in the same way the correlation length of Hermitian interacting non-random systems[2]. We show for the Hubbard model and the antiferromagnetic XXZ model in one dimension that the non-Hermitian critical point of the ground state, where the energy gap vanishes, is equal to the inverse correlation length. We also show that the conjecture is consistent with numerical results for S=1/2 frustrated quantum spin chains with the nearest- and next-nearest-neighbor interactions including the Majumdar-Ghosh model[3]. [1] N. Hatano and D. R. Nelson, PRL 77 (1996) 570; PRB 56 (1997) 8651. [2] Y. Nakamura and N. Hatano, Physica B, accepted. [3] C. K. Majumdar and D. K. Ghosh, J. Phys. C3 (1970) 911; J. Math. Phys. 10 (1969) 1388, 1399.

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

The Representation of Comparative Relations and the Transitive Inference Task

ERIC Educational Resources Information Center

Riley, Christine A.

1976-01-01

The question of how children represent and use comparative or partially ordered information is examined. Two experiments tested a conjecture that a common representation, a linear order, underlies the processing of all comparatives. (Author/MS)

New construction of eigenstates and separation of variables for SU( N) quantum spin chains

NASA Astrophysics Data System (ADS)

Gromov, Nikolay; Levkovich-Maslyuk, Fedor; Sizov, Grigory

2017-09-01

We conjecture a new way to construct eigenstates of integrable XXX quantum spin chains with SU( N) symmetry. The states are built by repeatedly acting on the vacuum with a single operator B good( u) evaluated at the Bethe roots. Our proposal serves as a compact alternative to the usual nested algebraic Bethe ansatz. Furthermore, the roots of this operator give the separated variables of the model, explicitly generalizing Sklyanin's approach to the SU( N) case. We present many tests of the conjecture and prove it in several special cases. We focus on rational spin chains with fundamental representation at each site, but expect many of the results to be valid more generally.

Cognition and Language: From Apprehension to Judgment -- Quantum Conjectures

NASA Astrophysics Data System (ADS)

Arecchi, F. T.

2014-12-01

We critically discuss the two moments of human cognition, namely, apprehension (A), whereby a coherent perception emerges from the recruitment of neuronal groups, and judgment (B), that entails the comparison of two apprehensions acquired at different times, coded in a suitable language and recalled by memory. (B) requires selfconsciousness, in so far as the agent who expresses the judgment must be aware that the two apprehensions are submitted to his/her own scrutiny and that it is his/her duty to extract a mutual relation. Since (B) lasts around 3 seconds, the semantic value of the pieces under comparison must be decided within this time. This implies a fast search of the memory contents. As a fact, exploring human subjects with sequences of simple words, we find evidence of a limited time window, corresponding to the memory retrieval of a linguistic item in order to match it with the next one in a text flow (be it literary, or musical,or figurative). Classifying the information content of spike trains, an uncertainty relation emerges between the bit size of a word and its duration. This uncertainty is ruled by a constant that can be given a numerical value and that has nothing to do with Planck's constant. A "quantum conjecture" in the above sense might explain the onset and decay of the memory window connecting successive pieces of a linguistic text. The conjecture here formulated is applicable to other reported evidences of quantum effects in human cognitive processes, so far lacking a plausible framework since no efforts to assign a quantum constant have been associated.

Averages of ratios of the Riemann zeta-function and correlations of divisor sums

NASA Astrophysics Data System (ADS)

Conrey, Brian; Keating, Jonathan P.

2017-10-01

Nonlinearity has published articles containing a significant number-theoretic component since the journal was first established. We examine one thread, concerning the statistics of the zeros of the Riemann zeta function. We extend this by establishing a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of Möbius and divisor functions. Specifically, we prove that the ratios conjecture and an arithmetic correlations conjecture imply the same result. This provides new support for the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. Our main theorem generalises a recent calculation pertaining to the special case of two-over-two ratios.

On the degree conjecture for separability of multipartite quantum states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-15

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matricesmore » match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.« less

Exploring Duopoly Markets with Conjectural Variations

ERIC Educational Resources Information Center

Julien, Ludovic A.; Musy, Olivier; Saïdi, Aurélien W.

2014-01-01

In this article, the authors investigate competitive firm behaviors in a two-firm environment assuming linear cost and demand functions. By introducing conjectural variations, they capture the different market structures as specific configurations of a more general model. Conjectural variations are based on the assumption that each firm believes…

The Process of Student Cognition in Constructing Mathematical Conjecture

ERIC Educational Resources Information Center

Astawa, I. Wayan Puja; Budayasa, I. Ketut; Juniati, Dwi

2018-01-01

This research aims to describe the process of student cognition in constructing mathematical conjecture. Many researchers have studied this process but without giving a detailed explanation of how students understand the information to construct a mathematical conjecture. The researchers focus their analysis on how to construct and prove the…

Finding Conjectures Using Geometer's Sketchpad

ERIC Educational Resources Information Center

Fallstrom, Scott; Walter, Marion

2011-01-01

Conjectures, theorems, and problems in print often appear to come out of nowhere. Scott Fallstrom and Marion Walter describe how their thinking and conjectures evolved; they try to show how collaboration helped expand their ideas. By showing the results from working together, they hope readers will encourage collaboration amongst their students.…

2-D Breathers and Applications

NASA Astrophysics Data System (ADS)

Marín, J. L.; Eilbeck, J. C.; Russell, F. M.

In this chapter we show how a new type of nonlinear lattice excitation is helping to understand the long-standing puzzle of unexplained dark lines in crystals of muscovite mica. In fact, it was the conjecture that some kind of quasi-one-dimensional lattice soliton was responsible for those lines which led to the discovery of this new family of lattice excitations: mobile localized breathers of longitudinal type. We explore several properties of these moving breathers, both by numerical methods and by experimenting with analogue models. The results suggest a much broader application than just the mica problem.

Unitary subsector of generalized minimal models

NASA Astrophysics Data System (ADS)

Behan, Connor

2018-05-01

We revisit the line of nonunitary theories that interpolate between the Virasoro minimal models. Numerical bootstrap applications have brought about interest in the four-point function involving the scalar primary of lowest dimension. Using recent progress in harmonic analysis on the conformal group, we prove the conjecture that global conformal blocks in this correlator appear with positive coefficients. We also compute many such coefficients in the simplest mixed correlator system. Finally, we comment on the status of using global conformal blocks to isolate the truly unitary points on this line.

From Flashes to Edges to Objects: Recovery of Local Edge Fragments Initiates Spatiotemporal Boundary Formation

PubMed Central

Erlikhman, Gennady; Kellman, Philip J.

2016-01-01

Spatiotemporal boundary formation (SBF) is the perception of illusory boundaries, global form, and global motion from spatially and temporally sparse transformations of texture elements (Shipley and Kellman, 1993a, 1994; Erlikhman and Kellman, 2015). It has been theorized that the visual system uses positions and times of element transformations to extract local oriented edge fragments, which then connect by known interpolation processes to produce larger contours and shapes in SBF. To test this theory, we created a novel display consisting of a sawtooth arrangement of elements that disappeared and reappeared sequentially. Although apparent motion along the sawtooth would be expected, with appropriate spacing and timing, the resulting percept was of a larger, moving, illusory bar. This display approximates the minimal conditions for visual perception of an oriented edge fragment from spatiotemporal information and confirms that such events may be initiating conditions in SBF. Using converging objective and subjective methods, experiments showed that edge formation in these displays was subject to a temporal integration constraint of ~80 ms between element disappearances. The experiments provide clear support for models of SBF that begin with extraction of local edge fragments, and they identify minimal conditions required for this process. We conjecture that these results reveal a link between spatiotemporal object perception and basic visual filtering. Motion energy filters have usually been studied with orientation given spatially by luminance contrast. When orientation is not given in static frames, these same motion energy filters serve as spatiotemporal edge filters, yielding local orientation from discrete element transformations over time. As numerous filters of different characteristic orientations and scales may respond to any simple SBF stimulus, we discuss the aperture and ambiguity problems that accompany this conjecture and how they might be resolved by the visual system. PMID:27445886

Sound radiation from a high speed axial flow fan due to the inlet turbulence quadrupole interaction

NASA Technical Reports Server (NTRS)

Goldstein, M. E.; Rosenbaum, B. M.; Albers, L. U.

1974-01-01

A formula is obtained for the total acoustic power spectra radiated out the front of the fan as a function of frequency. The formula involves the design parameters of the fan as well as the statistical properties of the incident turbulence. Numerical results are calculated for values of the parameters in the range of interest for quiet fans tested at the Lewis Research Center. As in the dipole analysis, when the turbulence correlation lengths become equal to the interblade spacing, the predicted spectra exhibit peaks around the blade passing frequency and its harmonics. There has recently been considerable conjecture about whether the stretching of turbulent eddies as they enter a stationary fan could result in the inlet turbulence being the dominant source of pure tones from nontranslating fans. The results of the current analysis show that, unless the turbulent eddies become quite elongated, this noise source contributes predominantly to the broadband spectrum.

Dropout dynamics in pulsed quantum dot lasers due to mode jumping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sokolovskii, G. S.; Dudelev, V. V.; Deryagin, A. G.

2015-06-29

We examine the response of a pulse pumped quantum dot laser both experimentally and numerically. As the maximum of the pump pulse comes closer to the excited-state threshold, the output pulse shape becomes unstable and leads to dropouts. We conjecture that these instabilities result from an increase of the linewidth enhancement factor α as the pump parameter comes close to the excitated state threshold. In order to analyze the dynamical mechanism of the dropout, we consider two cases for which the laser exhibits either a jump to a different single mode or a jump to fast intensity oscillations. The originmore » of these two instabilities is clarified by a combined analytical and numerical bifurcation diagram of the steady state intensity modes.« less

Radial restricted solid-on-solid and etching interface-growth models

NASA Astrophysics Data System (ADS)

Alves, Sidiney G.

2018-03-01

An approach to generate radial interfaces is presented. A radial network recursively obtained is used to implement discrete model rules designed originally for the investigation in flat substrates. I used the restricted solid-on-solid and etching models as to test the proposed scheme. The results indicate the Kardar, Parisi, and Zhang conjecture is completely verified leading to a good agreement between the interface radius fluctuation distribution and the Gaussian unitary ensemble. The evolution of the radius agrees well with the generalized conjecture, and the two-point correlation function exhibits also a good agreement with the covariance of the Airy2 process. The approach can be used to investigate radial interfaces evolution for many other classes of universality.

The Weyl law for contractive maps

NASA Astrophysics Data System (ADS)

Spina, Maria E.; Rivas, Alejandro M. F.; Carlo, Gabriel

2013-11-01

We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps.

Discrimination of binocular color mixtures in dichromacy: evaluation of the Maxwell-Cornsweet conjecture

NASA Astrophysics Data System (ADS)

Knoblauch, Kenneth; McMahon, Matthew J.

1995-10-01

We tested the Maxwell-Cornsweet conjecture that differential spectral filtering of the two eyes can increase the dimensionality of a dichromat's color vision. Sex-linked dichromats wore filters that differentially passed long- and middle-wavelength regions of the spectrum to each eye. Monocularly, temporal modulation thresholds (1.5 Hz) for color mixtures from the Rayleigh region of the spectrum were accounted for by a single, univariant mechanism. Binocularly, univariance was rejected because, as in monocular viewing by trichromats, in no color direction could silent substitution of the color mixtures be obtained. Despite the filter-aided increase in dimension, estimated wavelength discrimination was quite poor in this spectral region, suggesting a limit to the effectiveness of this technique. binocular summation.

Radial restricted solid-on-solid and etching interface-growth models.

PubMed

Alves, Sidiney G

2018-03-01

An approach to generate radial interfaces is presented. A radial network recursively obtained is used to implement discrete model rules designed originally for the investigation in flat substrates. I used the restricted solid-on-solid and etching models as to test the proposed scheme. The results indicate the Kardar, Parisi, and Zhang conjecture is completely verified leading to a good agreement between the interface radius fluctuation distribution and the Gaussian unitary ensemble. The evolution of the radius agrees well with the generalized conjecture, and the two-point correlation function exhibits also a good agreement with the covariance of the Airy_{2} process. The approach can be used to investigate radial interfaces evolution for many other classes of universality.

Evolution of complexity following a global quench

NASA Astrophysics Data System (ADS)

Moosa, Mudassir

2018-03-01

The rate of complexification of a quantum state is conjectured to be bounded from above by the average energy of the state. A different conjecture relates the complexity of a holographic CFT state to the on-shell gravitational action of a certain bulk region. We use `complexity equals action' conjecture to study the time evolution of the complexity of the CFT state after a global quench. We find that the rate of growth of complexity is not only consistent with the conjectured bound, but it also saturates the bound soon after the system has achieved local equilibrium.

Modelling of and Conjecturing on a Soccer Ball in a Korean Eighth Grade Mathematics Classroom

ERIC Educational Resources Information Center

Lee, Kyeong-Hwa

2011-01-01

The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…

Checking the Goldbach conjecture up to 4\\cdot 10^11

NASA Astrophysics Data System (ADS)

Sinisalo, Matti K.

1993-10-01

One of the most studied problems in additive number theory, Goldbach's conjecture, states that every even integer greater than or equal to 4 can be expressed as a sum of two primes. In this paper checking of this conjecture up to 4 \\cdot {10^{11}} by the IBM 3083 mainframe with vector processor is reported.

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

Cryptography: Cracking Codes.

ERIC Educational Resources Information Center

Myerscough, Don; And Others

1996-01-01

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)

Technology Tips: Investigating Extrema with GeoGebra

ERIC Educational Resources Information Center

Cullen, Craig J.; Hertel, Joshua T.; John, Sheryl

2013-01-01

The NCTM Algebra Standard suggests that students use technology to explore the effects of varying the parameters in y = ax2 + bx + c. This article discusses an extension of this task that incorporates dynamic geometry software to engage students in generating, testing, and proving mathematical conjectures.

Children's Mathematical Reasoning: Opportunities for Developing Understanding and Creative Thinking

ERIC Educational Resources Information Center

Vale, Colleen; Bragg, Leicha A.; Widjaja, Wanty; Herbert, Sandra; Loong, Esther Yook-Kin

2017-01-01

Reasoning underpins students' mathematical understanding and promotes creative thinking. It is regarded as a key mathematical proficiency. This article discusses the reasoning actions that primary children employed and teachers noticed for the "What else belongs?" task focused on forming and testing conjectures.

Competition among cooperators: Altruism and reciprocity

PubMed Central

Danielson, Peter

2002-01-01

Levine argues that neither self-interest nor altruism explains experimental results in bargaining and public goods games. Subjects' preferences appear also to be sensitive to their opponents' perceived altruism. Sethi and Somanathan provide a general account of reciprocal preferences that survive under evolutionary pressure. Although a wide variety of reciprocal strategies pass this evolutionary test, Sethi and Somanthan conjecture that fewer are likely to survive when reciprocal strategies compete with each other. This paper develops evolutionary agent-based models to test their conjecture in cases where reciprocal preferences can differ in a variety of games. We confirm that reciprocity is necessary but not sufficient for optimal cooperation. We explore the theme of competition among reciprocal cooperators and display three interesting emergent organizations: racing to the “moral high ground,” unstable cycles of preference change, and, when we implement reciprocal mechanisms, hierarchies resulting from exploiting fellow cooperators. If reciprocity is a basic mechanism facilitating cooperation, we can expect interaction that evolves around it to be complex, non-optimal, and resistant to change. PMID:12011403

Analysis of the Cognitive Unity or Rupture between Conjecture and Proof When Learning to Prove on a Grade 10 Trigonometry Course

ERIC Educational Resources Information Center

Fiallo, Jorge; Gutiérrez, Angel

2017-01-01

We present results from a classroom-based intervention designed to help a class of grade 10 students (14-15 years old) learn proof while studying trigonometry in a dynamic geometry software environment. We analysed some students' solutions to conjecture-and-proof problems that let them gain experience in stating conjectures and developing proofs.…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qin, Hong; Liu, Jian; Xiao, Jianyuan

Particle-in-cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretising its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g. 10(9), degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinearmore » Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.« less

Infrared computations of defect Schur indices

DOE PAGES

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng

2016-11-18

We conjecture a formula for the Schur index of four-dimensional N = 2 theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free. We use the conjecture to compute these defect-enriched Schur indices for theories which lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate in various examples that line defect indices can be expressed as sums of characters of the associated two-dimensional chiral algebramore » and that for Argyres-Douglas theories the line defect OPE reduces in the index to the Verlinde algebra.« less

Infrared computations of defect Schur indices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng

We conjecture a formula for the Schur index of four-dimensional N = 2 theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free. We use the conjecture to compute these defect-enriched Schur indices for theories which lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate in various examples that line defect indices can be expressed as sums of characters of the associated two-dimensional chiral algebramore » and that for Argyres-Douglas theories the line defect OPE reduces in the index to the Verlinde algebra.« less

Moral consequences of becoming unemployed

PubMed Central

Barr, Abigail; Miller, Luis; Ubeda, Paloma

2016-01-01

We test the conjecture that becoming unemployed erodes the extent to which a person acknowledges earned entitlement. We use behavioral experiments to generate incentive-compatible measures of individuals’ tendencies to acknowledge earned entitlement and incorporate these experiments in a two-stage study. In the first stage, participants’ acknowledgment of earned entitlement was measured by engaging them in the behavioral experiments, and their individual employment status and other relevant socioeconomic characteristics were recorded. In the second stage, a year later, the process was repeated using the same instruments. The combination of the experimentally generated data and the longitudinal design allows us to investigate our conjecture using a difference-in-difference approach, while ruling out the pure self-interest confound. We report evidence consistent with a large, negative effect of becoming unemployed on the acknowledgment of earned entitlement. PMID:27071100

Drift of Phase Fluctuations in the ABC Model

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Buttà, Paolo

2013-07-01

In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they guessed to be an antisymmetric function of the three densities. By assuming the validity of the fluctuating hydrodynamic approximation, we prove the presence of such a drift, providing an analytical expression for it. This expression is then shown to be an antisymmetric function of the three densities. The antisymmetry of the drift can also be inferred from a symmetry property of the underlying microscopic dynamics.

Pressure and Temperature Sensors Using Two Spin Crossover Materials.

PubMed

Jureschi, Catalin-Maricel; Linares, Jorge; Boulmaali, Ayoub; Dahoo, Pierre Richard; Rotaru, Aurelian; Garcia, Yann

2016-02-02

The possibility of a new design concept for dual spin crossover based sensors for concomitant detection of both temperature and pressure is presented. It is conjectured from numerical results obtained by mean field approximation applied to a Ising-like model that using two different spin crossover compounds containing switching molecules with weak elastic interactions it is possible to simultaneously measure P and T. When the interaction parameters are optimized, the spin transition is gradual and for each spin crossover compounds, both temperature and pressure values being identified from their optical densities. This concept offers great perspectives for smart sensing devices.

The refined Swampland Distance Conjecture in Calabi-Yau moduli spaces

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Klaewer, Daniel; Schlechter, Lorenz; Wolf, Florian

2018-06-01

The Swampland Distance Conjecture claims that effective theories derived from a consistent theory of quantum gravity only have a finite range of validity. This will imply drastic consequences for string theory model building. The refined version of this conjecture says that this range is of the order of the naturally built in scale, namely the Planck scale. It is investigated whether the Refined Swampland Distance Conjecture is consistent with proper field distances arising in the well understood moduli spaces of Calabi-Yau compactification. Investigating in particular the non-geometric phases of Kähler moduli spaces of dimension h 11 ∈ {1 , 2 , 101}, we always find proper field distances that are smaller than the Planck-length.

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space

NASA Astrophysics Data System (ADS)

Crisford, Toby; Santos, Jorge E.

2017-05-01

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space.

PubMed

Crisford, Toby; Santos, Jorge E

2017-05-05

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

Yang-Baxter deformations of W2,4 × T1,1 and the associated T-dual models

NASA Astrophysics Data System (ADS)

Sakamoto, Jun-ichi; Yoshida, Kentaroh

2017-08-01

Recently, for principal chiral models and symmetric coset sigma models, Hoare and Tseytlin proposed an interesting conjecture that the Yang-Baxter deformations with the homogeneous classical Yang-Baxter equation are equivalent to non-abelian T-dualities with topological terms. It is significant to examine this conjecture for non-symmetric (i.e., non-integrable) cases. Such an example is the W2,4 ×T 1 , 1 background. In this note, we study Yang-Baxter deformations of type IIB string theory defined on W2,4 ×T 1 , 1 and the associated T-dual models, and show that this conjecture is valid even for this case. Our result indicates that the conjecture would be valid beyond integrability.

Vertex operator algebras of Argyres-Douglas theories from M5-branes

NASA Astrophysics Data System (ADS)

Song, Jaewon; Xie, Dan; Yan, Wenbin

2017-12-01

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type J on a punctured sphere. We denote the AD theories as ( J b [ k], Y), where J b [ k] and Y represent an irregular and a regular singularity respectively. We restrict to the `minimal' case where J b [ k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra W^{k_{2d}}(J, Y ) , where {k}_{2d}=-h+b/b+k with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b = h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.

A restricted proof that the weak equivalence principle implies the Einstein equivalence principle

NASA Technical Reports Server (NTRS)

Lightman, A. P.; Lee, D. L.

1973-01-01

Schiff has conjectured that the weak equivalence principle (WEP) implies the Einstein equivalence principle (EEP). A proof is presented of Schiff's conjecture, restricted to: (1) test bodies made of electromagnetically interacting point particles, that fall from rest in a static, spherically symmetric gravitational field; (2) theories of gravity within a certain broad class - a class that includes almost all complete relativistic theories that have been found in the literature, but with each theory truncated to contain only point particles plus electromagnetic and gravitational fields. The proof shows that every nonmentric theory in the class (every theory that violates EEP) must violate WEP. A formula is derived for the magnitude of the violation. It is shown that WEP is a powerful theoretical and experimental tool for constraining the manner in which gravity couples to electromagnetism in gravitation theories.

Diagnosing a Failed Proof in Fault-Tolerance: A Disproving Challenge Problem

NASA Technical Reports Server (NTRS)

Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo

2006-01-01

This paper proposes a challenge problem in disproving. We describe a fault-tolerant distributed protocol designed at NASA for use in a fly-by-wire system for next-generation commercial aircraft. An early design of the protocol contains a subtle bug that is highly unlikely to be caught in fault injection testing. We describe a failed proof of the protocol's correctness in a mechanical theorem prover (PVS) with a complex unfinished proof conjecture. We use a model checking suite (SAL) to generate a concrete counterexample to the unproven conjecture to demonstrate the existence of a bug. However, we argue that the effort required in our approach is too high and propose what conditions a better solution would satisfy. We carefully describe the protocol and bug to provide a challenging but feasible case study for disproving research.

Thermodynamics with pressure and volume under charged particle absorption

NASA Astrophysics Data System (ADS)

Gwak, Bogeun

2017-11-01

We investigate the variation of the charged anti-de Sitter black hole under charged particle absorption by considering thermodynamic volume. When the energy of the particle is considered to contribute to the internal energy of the black hole, the variation exactly corresponds to the prediction of the first law of thermodynamics. Nevertheless, we find the decrease of the Bekenstein-Hawking entropy for extremal and near-extremal black holes under the absorption, which is an irreversible process. This violation of the second law of thermodynamics is only found when considering thermodynamic volume. We test the weak cosmic censorship conjecture affected by the violation. Fortunately, the conjecture is still valid, but extremal and near-extremal black holes do not change their configurations when any particle enters the black hole. This result is quite different from the case in which thermodynamic volume is not considered.

Reviving the shear-free perfect fluid conjecture in general relativity

NASA Astrophysics Data System (ADS)

Sikhonde, Muzikayise E.; Dunsby, Peter K. S.

2017-12-01

Employing a Mathematica symbolic computer algebra package called xTensor, we present (1+3) -covariant special case proofs of the shear-free perfect fluid conjecture in general relativity. We first present the case where the pressure is constant, and where the acceleration is parallel to the vorticity vector. These cases were first presented in their covariant form by Senovilla et al. We then provide a covariant proof for the case where the acceleration and vorticity vectors are orthogonal, which leads to the existence of a Killing vector along the vorticity. This Killing vector satisfies the new constraint equations resulting from the vanishing of the shear. Furthermore, it is shown that in order for the conjecture to be true, this Killing vector must have a vanishing spatially projected directional covariant derivative along the velocity vector field. This in turn implies the existence of another basic vector field along the direction of the vorticity for the conjecture to hold. Finally, we show that in general, there exists a basic vector field parallel to the acceleration for which the conjecture is true.

Coupled skinny baker's maps and the Kaplan-Yorke conjecture

NASA Astrophysics Data System (ADS)

Gröger, Maik; Hunt, Brian R.

2013-09-01

The Kaplan-Yorke conjecture states that for ‘typical’ dynamical systems with a physical measure, the information dimension and the Lyapunov dimension coincide. We explore this conjecture in a neighborhood of a system for which the two dimensions do not coincide because the system consists of two uncoupled subsystems. We are interested in whether coupling ‘typically’ restores the equality of the dimensions. The particular subsystems we consider are skinny baker's maps, and we consider uni-directional coupling. For coupling in one of the possible directions, we prove that the dimensions coincide for a prevalent set of coupling functions, but for coupling in the other direction we show that the dimensions remain unequal for all coupling functions. We conjecture that the dimensions prevalently coincide for bi-directional coupling. On the other hand, we conjecture that the phenomenon we observe for a particular class of systems with uni-directional coupling, where the information and Lyapunov dimensions differ robustly, occurs more generally for many classes of uni-directionally coupled systems (also called skew-product systems) in higher dimensions.

Critical points of the O(n) loop model on the martini and the 3-12 lattices

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Fu, Zhe; Guo, Wenan

2012-06-01

We derive the critical line of the O(n) loop model on the martini lattice as a function of the loop weight n basing on the critical points on the honeycomb lattice conjectured by Nienhuis [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.49.1062 49, 1062 (1982)]. In the limit n→0 we prove the connective constant μ=1.7505645579⋯ of self-avoiding walks on the martini lattice. A finite-size scaling analysis based on transfer matrix calculations is also performed. The numerical results coincide with the theoretical predictions with a very high accuracy. Using similar numerical methods, we also study the O(n) loop model on the 3-12 lattice. We obtain similarly precise agreement with the critical points given by Batchelor [J. Stat. Phys.JSTPBS0022-471510.1023/A:1023065215233 92, 1203 (1998)].

Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics

NASA Technical Reports Server (NTRS)

Fyfe, D.; Joyce, G.; Montgomery, D.

1976-01-01

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing, a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wave numbers simultaneously with a cascade of mean square vector potential to lower wave numbers, leading to an omni-directional magnetic energy spectrum which varies as 1/k 3 at lower wave numbers, simultaneously with a buildup of magnetic excitation at the lowest wave number of the system. Equipartition of kinetic and magnetic energies is expected at the highest wave numbers in the system.

Multi-loop positivity of the planar $$ \\mathcal{N} $$ = 4 SYM six-point amplitude

DOE PAGES

Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.; ...

2017-02-22

We study the six-point NMHV ratio function in planarmore » $$ \\mathcal{N} $$ = 4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a “radial” direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.« less

On the validity of cosmic no-hair conjecture in an anisotropic inationary model

NASA Astrophysics Data System (ADS)

Do, Tuan Q.

2018-05-01

We will present main results of our recent investigations on the validity of cosmic no-hair conjecture proposed by Hawking and his colleagues long time ago in the framework of an anisotropic inflationary model proposed by Kanno, Soda, and Watanabe. As a result, we will show that the cosmic no-hair conjecture seems to be generally violated in the Kanno-Soda- Watanabe model for both canonical and non-canonical scalar fields due to the existence of a non-trivial coupling term between scalar and electromagnetic fields. However, we will also show that the validity of the cosmic no-hair conjecture will be ensured once a unusual scalar field called the phantom field, whose kinetic energy term is negative definite, is introduced into the Kanno-Soda-Watanabe model.

Bartnik’s splitting conjecture and Lorentzian Busemann function

NASA Astrophysics Data System (ADS)

Amini, Roya; Sharifzadeh, Mehdi; Bahrampour, Yousof

2018-05-01

In 1988 Bartnik posed the splitting conjecture about the cosmological space-time. This conjecture has been proved by several people, with different approaches and by using some additional assumptions such as ‘S-ray condition’ and ‘level set condition’. It is known that the ‘S-ray condition’ yields the ‘level set condition’. We have proved that the two are indeed equivalent, by giving a different proof under the assumption of the ‘level set condition’. In addition, we have shown several properties of the cosmological space-time, under the presence of the ‘level set condition’. Finally we have provided a proof of the conjecture under a different assumption on the cosmological space-time. But we first prove some results without the timelike convergence condition which help us to state our proofs.

Debt, Democratization, and Development in Latin America: How Policy Can Affect Global Warming

ERIC Educational Resources Information Center

Aubourg, Rene W.; Good, David H.; Krutilla, Kerry

2008-01-01

The environmental Kuznets curve (EKC) hypothesis conjectures a nonlinear relationship between pollution and economic growth, such that pollution per capita initially increases as countries economically develop, but then reaches a maximum point before ultimately declining. Much of the EKC literature has focused on testing this basic hypothesis and,…

Women's Benevolent Sexism as Reaction to Hostility

ERIC Educational Resources Information Center

Fischer, Ann R.

2006-01-01

Grounded in the theory of ambivalent sexism, this study tested the speculation that women's benevolent sexist attitudes may be, in part, a self-protective response to environments they perceive as hostile to women. Data that have indirectly supported this conjecture thus far have been correlational. The current study involved a more powerful,…

Solving Optimization Problems with Dynamic Geometry Software: The Airport Problem

ERIC Educational Resources Information Center

Contreras, José

2014-01-01

This paper describes how the author's students (in-service and pre-service secondary mathematics teachers) enrolled in college geometry courses use the Geometers' Sketchpad (GSP) to gain insight to formulate, confirm, test, and refine conjectures to solve the classical airport problem for triangles. The students are then provided with strategic…

Experiencing Mathematics: Activities to Engage the High School Student. Teacher Edition

ERIC Educational Resources Information Center

Breunlin, R. James; Kasper, Timothy A.; Kolet, Michelle; Letzel, Kendra; Letzel, Thomas; Noah, John; Schutte, Jennifer; Williams, Bob; Zickert, Chris

2006-01-01

This book is the result of the collaborative effort of nine AYA National Board Certified Teachers in Mathematics. It represents a compilation of teacher-tested activities that prompt high school students to explore, conjecture and reflect on their mathematical adventures-- thus "experience mathematics." This edition will educate the teacher…

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

Critical end point in the presence of a chiral chemical potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Z. -F.; Cloët, I. C.; Lu, Y.

A class of Polyakov-loop-modified Nambu-Jona-Lasinio models has been used to support a conjecture that numerical simulations of lattice-regularized QCD defined with a chiral chemical potential can provide information about the existence and location of a critical end point in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physicallymore » motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the Polyakov-loop-modified Nambu-Jona-Lasinio models and the four-fermion coupling in those models does not react strongly to changes in the mean field that is assumed to mock-up Polyakov-loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with mu(5) > 0 can shed any light on a critical end point in the regular QCD phase diagram.« less

Locality of correlation in density functional theory.

PubMed

Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano

2016-08-07

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

Rigorous Results for the Distribution of Money on Connected Graphs

NASA Astrophysics Data System (ADS)

Lanchier, Nicolas; Reed, Stephanie

2018-05-01

This paper is concerned with general spatially explicit versions of three stochastic models for the dynamics of money that have been introduced and studied numerically by statistical physicists: the uniform reshuffling model, the immediate exchange model and the model with saving propensity. All three models consist of systems of economical agents that consecutively engage in pairwise monetary transactions. Computer simulations performed in the physics literature suggest that, when the number of agents and the average amount of money per agent are large, the limiting distribution of money as time goes to infinity approaches the exponential distribution for the first model, the gamma distribution with shape parameter two for the second model and a distribution similar but not exactly equal to a gamma distribution whose shape parameter depends on the saving propensity for the third model. The main objective of this paper is to give rigorous proofs of these conjectures and also extend these conjectures to generalizations of the first two models and a variant of the third model that include local rather than global interactions, i.e., instead of choosing the two interacting agents uniformly at random from the system, the agents are located on the vertex set of a general connected graph and can only interact with their neighbors.

Eisenstein Hecke algebras and Iwasawa theory

NASA Astrophysics Data System (ADS)

Wake, Preston

We show that if an Eisenstein component of the p-adic Hecke algebra associated to modular forms is Gorenstein, then it is necessary that the plus-part of a certain ideal class group is trivial. We also show that this condition is sufficient whenever a conjecture of Sharifi holds. We also formulate a weaker Gorenstein property, and show that this weak Gorenstein property holds if and only if a weak form of Sharifi's conjecture and a weak form of Greenberg's conjecture hold.

Matrix Models and A Proof of the Open Analog of Witten's Conjecture

NASA Astrophysics Data System (ADS)

Buryak, Alexandr; Tessler, Ran J.

2017-08-01

In a recent work, R. Pandharipande, J. P. Solomon and the second author have initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection numbers satisfies the open KdV equations. In this paper we prove this conjecture. Our proof goes through a matrix model and is based on a Kontsevich type combinatorial formula for the intersection numbers that was found by the second author.

A bound on chaos

DOE PAGES

Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas

2016-08-17

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Stretchy binary classification.

PubMed

Toh, Kar-Ann; Lin, Zhiping; Sun, Lei; Li, Zhengguo

2018-01-01

In this article, we introduce an analytic formulation for compressive binary classification. The formulation seeks to solve the least ℓ p -norm of the parameter vector subject to a classification error constraint. An analytic and stretchable estimation is conjectured where the estimation can be viewed as an extension of the pseudoinverse with left and right constructions. Our variance analysis indicates that the estimation based on the left pseudoinverse is unbiased and the estimation based on the right pseudoinverse is biased. Sparseness can be obtained for the biased estimation under certain mild conditions. The proposed estimation is investigated numerically using both synthetic and real-world data. Copyright © 2017 Elsevier Ltd. All rights reserved.

Non-integrability vs. integrability in pentagram maps

NASA Astrophysics Data System (ADS)

Khesin, Boris; Soloviev, Fedor

2015-01-01

We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective duality. We show that in many cases the pentagram map cannot be included into integrable flows as a time-one map, and discuss how the corresponding notion of discrete integrability can be extended to include jumps between invariant tori. We also present a numerical evidence that certain generalizations of the integrable 2D pentagram map are non-integrable and present a conjecture for a necessary condition of their discrete integrability.

On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.

PubMed

Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio

2015-01-01

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

Strong monogamy conjecture in a four-qubit system

NASA Astrophysics Data System (ADS)

Karmakar, Sumana; Sen, Ajoy; Bhar, Amit; Sarkar, Debasis

2016-01-01

Monogamy is a defining feature of entanglement, having far-reaching applications. Recently, Regula et al. [Phys. Rev. Lett. 113, 110501 (2014), 10.1103/PhysRevLett.113.110501] proposed a stronger version of monogamy relation for concurrence. We have extended the strong monogamy inequality for another entanglement measure, viz., negativity. In particular, we have concentrated on the four-qubit system and provided a detailed study on the status of strong monogamy on pure states. Further, we have analytically provided some classes of states for which negativity and squared negativity satisfy strong monogamy. Numerical evidences have also been shown in proper places. Our analysis also provides cases where strong monogamy is violated.

Deciphering infant mortality

NASA Astrophysics Data System (ADS)

Berrut, Sylvie; Pouillard, Violette; Richmond, Peter; Roehner, Bertrand M.

2016-12-01

This paper is about infant mortality. In line with reliability theory, "infant" refers to the time interval following birth during which the mortality (or failure) rate decreases. This definition provides a systems science perspective in which birth constitutes a sudden transition falling within the field of application of the Transient Shock (TS) conjecture put forward in Richmond and Roehner (2016c). This conjecture provides predictions about the timing and shape of the death rate peak. It says that there will be a death rate spike whenever external conditions change abruptly and drastically and also predicts that after a steep rise there will be a much longer hyperbolic relaxation process. These predictions can be tested by considering living organisms for which the transient shock occurs several days after birth. Thus, for fish there are three stages: egg, yolk-sac and young adult phases. The TS conjecture predicts a mortality spike at the end of the yolk-sac phase and this timing is indeed confirmed by observation. Secondly, the hyperbolic nature of the relaxation process can be tested using very accurate Swiss statistics for postnatal death rates spanning the period from one hour immediately after birth through to age 10 years. It turns out that since the 19th century despite a significant and large reduction in infant mortality, the shape of the age-specific death rate has remained basically unchanged. Moreover the hyperbolic pattern observed for humans is also found for small primates as recorded in the archives of zoological gardens. Our overall objective is to identify a series of cases which start from simple systems and move step by step to more complex organisms. The cases discussed here we believe represent initial landmarks in this quest.

Model Checking Failed Conjectures in Theorem Proving: A Case Study

NASA Technical Reports Server (NTRS)

Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo

2004-01-01

Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.

Betti numbers of graded modules and cohomology of vector bundles

NASA Astrophysics Data System (ADS)

Eisenbud, David; Schreyer, Frank-Olaf

2009-07-01

In the remarkable paper Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, Mats Boij and Jonas Soederberg conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring is a positive linear combination of Betti tables of modules with pure resolutions. We prove a strengthened form of their conjectures. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fan naturally associated to the Young lattice. With the same tools we show that the cohomology table of any vector bundle on projective space is a positive rational linear combination of the cohomology tables of what we call supernatural vector bundles. Using this result we give new bounds on the slope of a vector bundle in terms of its cohomology.

An Entropy-Based Approach to Nonlinear Stability

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

The Cognitive Advantages of Counting Specifically: A Representational Analysis of Verbal Numeration Systems in Oceanic Languages.

PubMed

Bender, Andrea; Schlimm, Dirk; Beller, Sieghard

2015-10-01

The domain of numbers provides a paradigmatic case for investigating interactions of culture, language, and cognition: Numerical competencies are considered a core domain of knowledge, and yet the development of specifically human abilities presupposes cultural and linguistic input by way of counting sequences. These sequences constitute systems with distinct structural properties, the cross-linguistic variability of which has implications for number representation and processing. Such representational effects are scrutinized for two types of verbal numeration systems-general and object-specific ones-that were in parallel use in several Oceanic languages (English with its general system is included for comparison). The analysis indicates that the object-specific systems outperform the general systems with respect to counting and mental arithmetic, largely due to their regular and more compact representation. What these findings reveal on cognitive diversity, how the conjectures involved speak to more general issues in cognitive science, and how the approach taken here might help to bridge the gap between anthropology and other cognitive sciences is discussed in the conclusion. Copyright © 2015 Cognitive Science Society, Inc.

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

NASA Technical Reports Server (NTRS)

Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K.N.; Stamnes, K.

2016-01-01

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarized radiative transfer of a cirrus cloud consisting of randomly oriented hexagonal ice crystals: The 3×3 approximation for non-spherical particles

NASA Astrophysics Data System (ADS)

Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K. N.; Stamnes, K.

2017-05-01

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 ×103 so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling-adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5% for I and within 1.5% for Q for all viewing angles. In 1971 Hansen [1] showed that for scattering by spherical particles the 3×3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3×3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3×3 approximation leads to an absolute error < 2 ×10-6 for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braunstein, Samuel L.; Ghosh, Sibasish; Severini, Simone

We reconsider density matrices of graphs as defined in quant-ph/0406165. The density matrix of a graph is the combinatorial Laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the 'degree condition') to test the separability of density matrices of graphs. The condition is directly related to the Peres-Horodecki partial transposition condition. We prove that the degree condition is necessary for separability, and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest-point graphs and perfect matchings. We observe that the degree condition appears to have a value beyondmore » the density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. We isolate a number of problems and delineate further generalizations.« less

Gravitational entropy and the cosmological no-hair conjecture

NASA Astrophysics Data System (ADS)

Bolejko, Krzysztof

2018-04-01

The gravitational entropy and no-hair conjectures seem to predict contradictory future states of our Universe. The growth of the gravitational entropy is associated with the growth of inhomogeneity, while the no-hair conjecture argues that a universe dominated by dark energy should asymptotically approach a homogeneous and isotropic de Sitter state. The aim of this paper is to study these two conjectures. The investigation is based on the Simsilun simulation, which simulates the universe using the approximation of the Silent Universe. The Silent Universe is a solution to the Einstein equations that assumes irrotational, nonviscous, and insulated dust, with vanishing magnetic part of the Weyl curvature. The initial conditions for the Simsilun simulation are sourced from the Millennium simulation, which results with a realistically appearing but relativistic at origin simulation of a universe. The Simsilun simulation is evolved from the early universe (t =25 Myr ) until far future (t =1000 Gyr ). The results of this investigation show that both conjectures are correct. On global scales, a universe with a positive cosmological constant and nonpositive spatial curvature does indeed approach the de Sitter state. At the same time it keeps generating the gravitational entropy.

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Yao

Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To numerically resolve this issue, the schemes employed must preserve magnetic topology exactly to avoid artificial reconnection in the presence of (nearly) singular current densities. Structure-preserving numerical methods are favorable for mitigating numerical dissipation, and variational integration is a powerful machinery for deriving them. However, successful applications of variational integration to ideal MHD have been scarce. In thismore » thesis, we develop variational integrators for ideal MHD in Lagrangian labeling by discretizing Newcomb's Lagrangian on a moving mesh using discretized exterior calculus. With the built-in frozen-in equation, the schemes are free of artificial reconnection, hence optimal for studying current singularity formation. Using this method, we first study a fundamental prototype problem in 2D, the Hahm-Kulsrud-Taylor (HKT) problem. It considers the effect of boundary perturbations on a 2D plasma magnetized by a sheared field, and its linear solution is singular. We find that with increasing resolution, the nonlinear solution converges to one with a current singularity. The same signature of current singularity is also identified in other 2D cases with more complex magnetic topologies, such as the coalescence instability of magnetic islands. We then extend the HKT problem to 3D line-tied geometry, which models the solar corona by anchoring the field lines in the boundaries. The effect of such geometry is crucial in the controversy over Parker's conjecture. The linear solution, which is singular in 2D, is found to be smooth. However, with finite amplitude, it can become pathological above a critical system length. The nonlinear solution turns out smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. With the results in hand, we cannot confirm or rule out this possibility conclusively, since we cannot obtain solutions with system lengths near the extrapolated critical value.« less

Using Spreadsheets to Help Students Think Recursively

ERIC Educational Resources Information Center

Webber, Robert P.

2012-01-01

Spreadsheets lend themselves naturally to recursive computations, since a formula can be defined as a function of one of more preceding cells. A hypothesized closed form for the "n"th term of a recursive sequence can be tested easily by using a spreadsheet to compute a large number of the terms. Similarly, a conjecture about the limit of a series…

One-loop tests of supersymmetric gauge theories on spheres

DOE PAGES

Minahan, Joseph A.; Naseer, Usman

2017-07-14

Here, we show that a recently conjectured form for perturbative supersymmetric partition functions on spheres of general dimension d is consistent with the at space limit of 6-dimensional N = 1 super Yang-Mills. We also show that the partition functions for N = 1 8- and 9-dimensional theories are consistent with their known at space limits.

MENDEL: An Intelligent Computer Tutoring System for Genetics Problem-Solving, Conjecturing, and Understanding.

ERIC Educational Resources Information Center

Streibel, Michael; And Others

1987-01-01

Describes an advice-giving computer system being developed for genetics education called MENDEL that is based on research in learning, genetics problem solving, and expert systems. The value of MENDEL as a design tool and the tutorial function are stressed. Hypothesis testing, graphics, and experiential learning are also discussed. (Author/LRW)

Brown-York quasilocal energy in Lanczos-Lovelock gravity and black hole horizons

NASA Astrophysics Data System (ADS)

Chakraborty, Sumanta; Dadhich, Naresh

2015-12-01

A standard candidate for quasilocal energy in general relativity is the Brown-York energy, which is essentially a two dimensional surface integral of the extrinsic curvature on the two-boundary of a spacelike hypersurface referenced to flat spacetime. Several years back one of us had conjectured that the black hole horizon is defined by equipartition of gravitational and non-gravitational energy. By employing the above definition of quasilocal Brown-York energy, we have verified the equipartition conjecture for static charged and charged axi-symmetric black holes in general relativity. We have further generalized the Brown-York formalism to all orders in Lanczos-Lovelock theories of gravity and have verified the conjecture for pure Lovelock charged black hole in all even d = 2 m + 2 dimensions, where m is the degree of Lovelock action. It turns out that the equipartition conjecture works only for pure Lovelock, and not for Einstein-Lovelock black holes.

Small black holes and near-extremal CFTs

DOE PAGES

Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; ...

2016-08-02

Pure theories of AdS 3 quantum gravity are conjectured to be dual to CFTs with sparse spectra of light primary operators. The sparsest possible spectrum consistent with modular invariance includes only black hole states above the vacuum. Witten conjectured the existence of a family of extremal CFTs, which realize this spectrum for all admissible values of the central charge. We consider the quantum corrections to the classical spectrum, and propose a specific modification of Witten’s conjecture which takes into account the existence of “small” black hole states. These have zero classical horizon area, with a calculable entropy attributed solely tomore » loop effects. Lastly, our conjecture passes various consistency checks, especially when generalized to include theories with supersymmetry. In theories with N = 2 supersymmetry, this “near-extremal CFT” proposal precisely evades the no-go results of Gaberdiel et al.« less

A Hybrid Analytical/Numerical Model for the Characterization of Preferential Flow Path with Non-Darcy Flow

PubMed Central

Wang, Sen; Feng, Qihong; Han, Xiaodong

2013-01-01

Due to the long-term fluid-solid interactions in waterflooding, the tremendous variation of oil reservoir formation parameters will lead to the widespread evolution of preferential flow paths, thereby preventing the further enhancement of recovery efficiency because of unstable fingering and premature breakthrough. To improve oil recovery, the characterization of preferential flow paths is essential and imperative. In efforts that have been previously documented, fluid flow characteristics within preferential paths are assumed to obey Darcy's equation. However, the occurrence of non-Darcy flow behavior has been increasingly suggested. To examine this conjecture, the Forchheimer number with the inertial coefficient estimated from different empirical formulas is applied as the criterion. Considering a 10% non-Darcy effect, the fluid flow in a preferential path may do experience non-Darcy behavior. With the objective of characterizing the preferential path with non-Darcy flow, a hybrid analytical/numerical model has been developed to investigate the pressure transient response, which dynamically couples a numerical model describing the non-Darcy effect of a preferential flow path with an analytical reservoir model. The characteristics of the pressure transient behavior and the sensitivities of corresponding parameters have also been discussed. In addition, an interpretation approach for pressure transient testing is also proposed, in which the Gravitational Search Algorithm is employed as a non-linear regression technology to match measured pressure with this hybrid model. Examples of applications from different oilfields are also presented to illustrate this method. This cost-effective approach provides more accurate characterization of a preferential flow path with non-Darcy flow, which will lay a solid foundation for the design and operation of conformance control treatments, as well as several other Enhanced Oil Recovery projects. PMID:24386224

Conjectures on the relations of linking and causality in causally simple spacetimes

NASA Astrophysics Data System (ADS)

Chernov, Vladimir

2018-05-01

We formulate the generalization of the Legendrian Low conjecture of Natario and Tod (proved by Nemirovski and myself before) to the case of causally simple spacetimes. We prove a weakened version of the corresponding statement. In all known examples, a causally simple spacetime can be conformally embedded as an open subset into some globally hyperbolic and the space of light rays in is an open submanifold of the space of light rays in . If this is always the case, this provides an approach to solving the conjectures relating causality and linking in causally simple spacetimes.

Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves

NASA Astrophysics Data System (ADS)

Kanazawa, Atsushi

2017-04-01

We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of X can be constructed by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds. The two crucial ideas in our proof are to obtain a complex structure by gluing the underlying affine manifolds and to construct the theta functions from the Landau-Ginzburg superpotentials.

Symmetric moment problems and a conjecture of Valent

NASA Astrophysics Data System (ADS)

Berg, C.; Szwarc, R.

2017-03-01

In 1998 Valent made conjectures about the order and type of certain indeterminate Stieltjes moment problems associated with birth and death processes which have polynomial birth and death rates of degree {p≥slant 3}. Romanov recently proved that the order is 1/p as conjectured. We prove that the type with respect to the order is related to certain multi-zeta values and that this type belongs to the interval which also contains the conjectured value. This proves that the conjecture about type is asymptotically correct as p\\to∞. The main idea is to obtain estimates for order and type of symmetric indeterminate Hamburger moment problems when the orthonormal polynomials P_n and those of the second kind Q_n satisfy P2n^2(0)∼ c_1n-1/β and Q2n-1^2(0)∼ c2 n-1/α, where 0<α,β<1 may be different, and c_1 and c_2 are positive constants. In this case the order of the moment problem is majorized by the harmonic mean of α and β. Here α_n∼ β_n means that α_n/β_n\\to 1. This also leads to a new proof of Romanov's Theorem that the order is 1/p. Bibliography: 19 titles.

Notes on integral identities for 3d supersymmetric dualities

NASA Astrophysics Data System (ADS)

Aghaei, Nezhla; Amariti, Antonio; Sekiguchi, Yuta

2018-04-01

Four dimensional N=2 Argyres-Douglas theories have been recently conjectured to be described by N=1 Lagrangian theories. Such models, once reduced to 3d, should be mirror dual to Lagrangian N=4 theories. This has been numerically checked through the matching of the partition functions on the three sphere. In this article, we provide an analytic derivation for this result in the A 2 n-1 case via hyperbolic hypergeometric integrals. We study the D 4 case as well, commenting on some open questions and possible resolutions. In the second part of the paper we discuss other integral identities leading to the matching of the partition functions in 3d dual pairs involving higher monopole superpotentials.

Many-Particle Dephasing after a Quench

NASA Astrophysics Data System (ADS)

Kiendl, Thomas; Marquardt, Florian

2017-03-01

After a quench in a quantum many-body system, expectation values tend to relax towards long-time averages. However, temporal fluctuations remain in the long-time limit, and it is crucial to study the suppression of these fluctuations with increasing system size. The particularly important case of nonintegrable models has been addressed so far only by numerics and conjectures based on analytical bounds. In this work, we are able to derive analytical predictions for the temporal fluctuations in a nonintegrable model (the transverse Ising chain with extra terms). Our results are based on identifying a dynamical regime of "many-particle dephasing," where quasiparticles do not yet relax but fluctuations are nonetheless suppressed exponentially by weak integrability breaking.

Many-Particle Dephasing after a Quench.

PubMed

Kiendl, Thomas; Marquardt, Florian

2017-03-31

After a quench in a quantum many-body system, expectation values tend to relax towards long-time averages. However, temporal fluctuations remain in the long-time limit, and it is crucial to study the suppression of these fluctuations with increasing system size. The particularly important case of nonintegrable models has been addressed so far only by numerics and conjectures based on analytical bounds. In this work, we are able to derive analytical predictions for the temporal fluctuations in a nonintegrable model (the transverse Ising chain with extra terms). Our results are based on identifying a dynamical regime of "many-particle dephasing," where quasiparticles do not yet relax but fluctuations are nonetheless suppressed exponentially by weak integrability breaking.

American Mathematics from 1940 to the Day Before Yesterday

ERIC Educational Resources Information Center

Ewing, J. H.; And Others

1976-01-01

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane.

PubMed

Liu, T Y; Chiu, T L; Clarkson, P A; Chow, K W

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

Locality of correlation in density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burke, Kieron; Cancio, Antonio; Gould, Tim

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ +more » B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.« less

More N =4 superconformal bootstrap

NASA Astrophysics Data System (ADS)

Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C.

2017-08-01

In this long overdue second installment, we continue to develop the conformal bootstrap program for N =4 superconformal field theories (SCFTs) in four dimensions via an analysis of the correlation function of four stress-tensor supermultiplets. We review analytic results for this correlator and make contact with the SCFT/chiral algebra correspondence of Beem et al. [Commun. Math. Phys. 336, 1359 (2015), 10.1007/s00220-014-2272-x]. We demonstrate that the constraints of unitarity and crossing symmetry require the central charge c to be greater than or equal to 3 /4 in any interacting N =4 SCFT. We apply numerical bootstrap methods to derive upper bounds on scaling dimensions and operator product expansion coefficients for several low-lying, unprotected operators as a function of the central charge. We interpret our bounds in the context of N =4 super Yang-Mills theories, formulating a series of conjectures regarding the embedding of the conformal manifold—parametrized by the complexified gauge coupling—into the space of scaling dimensions and operator product expansion coefficients. Our conjectures assign a distinguished role to points on the conformal manifold that are self-dual under a subgroup of the S -duality group. This paper contains a more detailed exposition of a number of results previously reported in Beem et al. [Phys. Rev. Lett. 111, 071601 (2013), 10.1103/PhysRevLett.111.071601] in addition to new results.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane

NASA Astrophysics Data System (ADS)

Liu, T. Y.; Chiu, T. L.; Clarkson, P. A.; Chow, K. W.

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

Dynamical analysis of a cubic Liénard system with global parameters (II)

NASA Astrophysics Data System (ADS)

Chen, Hebai; Chen, Xingwu

2016-06-01

In this paper, we continue to study the global dynamics of a cubic Liénard system for global parameters in the case of three equilibria to follow (2015 Nonlinearity 28 3535-62), which deals with the case of two equilibria. We first analyse qualitative properties of all equilibria and judge the existences of limit cycles and homoclinic loops and their numbers. Then we obtain the bifurcation diagram and all phase portraits as our main results. Based on these results, in the case of three equilibria a positive answer to conjecture 3.2 of (1998 Nonlinearity 11 1505-19), which is about the existence of some function whose graph is exactly the surface of double limit cycles, is obtained. Moreover, a parameter region for the nonexistence of figure-eight loops is given theoretically to compensate for previous numerical results and is illustrated numerically. Supported by NSFC 11471228, 11572263, the Fundamental Research Funds for the Central Universities and Cultivation Foundation of Excellent Doctoral Dissertation of Southwest Jiaotong University (2015).

A Model for Displacements Between Parallel Plates That Shows Change of Type from Hyperbolic to Elliptic

NASA Astrophysics Data System (ADS)

Shariati, Maryam; Yortsos, Yannis; Talon, Laurent; Martin, Jerome; Rakotomalala, Nicole; Salin, Dominique

2003-11-01

We consider miscible displacement between parallel plates, where the viscosity is a function of the concentration. By selecting a piece-wise representation, the problem can be considered as ``three-phase'' flow. Assuming a lubrication-type approximation, the mathematical description is in terms of two quasi-linear hyperbolic equations. When the mobility of the middle phase is smaller than its neighbors, the system is genuinely hyperbolic and can be solved analytically. However, when it is larger, an elliptic region develops. This change-of-type behavior is for the first time proved here based on sound physical principles. Numerical solutions with a small diffusion are presented. Good agreement is obtained outside the elliptic region, but not inside, where the numerical results show unstable behavior. We conjecture that for the solution of the real problem in the mixed-type case, the full higher-dimensionality problem must be considered inside the elliptic region, in which the lubrication (parallel-flow) approximation is no longer appropriate. This is discussed in a companion presentation.

Studies in premixed combustion. [Benjamin Levich Inst. for Physico-Chemical Hydrodynamics, City College of CUNY, New York, New York

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sivashinsky, G.I.

1993-01-01

During the period under review, significant progress was been made in studying the intrinsic dynamics of premixed flames and the problems of flame-flow interaction. (1) A weakly nonlinear model for Bunsen burner stabilized flames was proposed and employed for the simulation of three-dimensional polyhedral flames -- one of the most graphic manifestations of thermal-diffusive instability in premixed combustion. (2) A high-precision large-scale numerical simulation of Bunsen burner tip structure was conducted. The results obtained supported the earlier conjecture that the tip opening observed in low Lewis number systems is a purely optical effect not involving either flame extinction or leakagemore » of unburned fuel. (3) A one-dimensional model describing a reaction wave moving through a unidirectional periodic flow field is proposed and studied numerically. For long-wavelength fields the system exhibits a peculiar non-uniqueness of possible propagation regimes. The transition from one regime to another occurs in a manner of hysteresis.« less

Thermodynamics of Inozemtsev's elliptic spin chain

NASA Astrophysics Data System (ADS)

Klabbers, Rob

2016-06-01

We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

Blood Flow in the Stenotic Carotid Bifurcation

NASA Astrophysics Data System (ADS)

Rayz, Vitaliy

2005-11-01

The carotid artery is prone to atherosclerotic disease and the growth of plaque in the vessel, leading often to severe occlusion or plaque rupture, resulting in emboli and thrombus, and, possibly, stroke. Modeling the flow in stenotic blood vessels can elucidate the influence of the flow on plaque growth and stability. Numerical simulations are carried out to model the complex flows in anatomically realistic, patient-specific geometries constructed from magnetic resonance images. The 3-D unsteady Navier-Stokes equations are solved in a finite-volume formulation, using an iterative pressure-correction algorithm. The flow field computed is highly three-dimensional, with high-speed jets and strong recirculating secondary flows. Sharp spatial and temporal variations of the velocities and shear stresses are observed. The results are in a good agreement with the available experimental and clinical data. The influence of non-Newtonian blood behavior and arterial wall compliance are considered. Transitional and turbulent regimes have been looked at using LES. This work supports the conjecture that numerical simulations can provide a diagnostic tool for assessing plaque stability.

Art, science and conjecture, from Hippocrates to Plato and Aristotle.

PubMed

Boudon-Millot, Véronique

2005-01-01

This paper attempts to study the notion of stochazesthai in the Hippocratic Corpus in relation to Hippocratic reflections on the status of the medical art. Considering the passages where the verb stochazesthai is employed, we can see that this word is not yet synonymous with the term "conjecture". The main point of interest are the relations between the Hippocratic writings and the relevant works of Plato and Aristotle. In revising the concept of stochazesthai in this way, it appears that this "conjectural" mode of knowledge was unknown to the Hippocratic writers and that it is really too early in their case to speak of "stochastic medicine".

A proof of the log-concavity conjecture related to the computation of the ergodic capacity of MIMO channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurvitis, Leonid

2009-01-01

An upper bound on the ergodic capacity of MIMO channels was introduced recently in [1]. This upper bound amounts to the maximization on the simplex of some multilinear polynomial p({lambda}{sub 1}, ..., {lambda}{sub n}) with non-negative coefficients. In general, such maximizations problems are NP-HARD. But if say, the functional log(p) is concave on the simplex and can be efficiently evaluated, then the maximization can also be done efficiently. Such log-concavity was conjectured in [1]. We give in this paper self-contained proof of the conjecture, based on the theory of H-Stable polynomials.

Testing the performance of a fragment of the COI gene to identify western Palaearctic stag beetle species (Coleoptera, Lucanidae).

PubMed

Cox, Karen; Thomaes, Arno; Antonini, Gloria; Zilioli, Michele; De Gelas, Koen; Harvey, Deborah; Solano, Emanuela; Audisio, Paolo; McKeown, Niall; Shaw, Paul; Minetti, Robert; Bartolozzi, Luca; Mergeay, Joachim

2013-12-30

Lucanidae) remains challenging, mainly due to the sexual dimorphism and the strong allometry in males. Such conjecture confounds taxonomic based conservation efforts that are urgently needed due to numerous threats to stag beetle biodiversity. Molecular tools could help solve the problem of identification of the different recognized taxa in the "Lucanus cervus complex" and in some related Palaearctic species. We investigated the potential use of a 670 bp region at the 3' end of the mitochondrial cytochrome c oxidase subunit I gene (COI) for barcoding purposes (different from the standard COI barcoding region). Well resolved species and subspecies were L. tetraodon, L. cervusakbesianus, L. c. laticornis, as well as the two eastern Asian outgroup taxa L. formosanus and L. hermani. Conversely, certain taxa could not be distinguished from each other based on K2P-distances and tree topologies: L. c. fabiani / L. (P.) barbarossa, L. c. judaicus / an unknown Lucanus species, L. c. cervus / L. c. turcicus / L. c. pentaphyllus / L. (P.) macrophyllus / L. ibericus. The relative roles of phenotypic plasticity, recurrent hybridisation and incomplete lineage sorting underlying taxonomic and phylogenetic discordances are discussed.

Improving the ideal and human observer consistency: a demonstration of principles

NASA Astrophysics Data System (ADS)

He, Xin

2017-03-01

In addition to being rigorous and realistic, the usefulness of the ideal observer computational tools may also depend on whether they serve the empirical purpose for which they are created, e.g. to identify desirable imaging systems to be used by human observers. In SPIE 10136-35, I have shown that the ideal and the human observers do not necessarily prefer the same system as the optimal or better one due to their different objectives in both hardware and software optimization. In this work, I attempt to identify a necessary but insufficient condition under which the human and the ideal observer may rank systems consistently. If corroborated, such a condition allows a numerical test on the ideal/human consistency without routine human observer studies. I reproduced data from Abbey et al. JOSA 2001 to verify the proposed condition (i.e., not a rigorous falsification study due to the lack of specificity in the proposed conjecture. A roadmap for more falsifiable conditions is proposed). Via this work, I would like to emphasize the reality of practical decision making in addition to the realism in mathematical modeling. (Disclaimer: the views expressed in this work do not necessarily represent those of the FDA.)

Numerical method for accessing the universal scaling function for a multiparticle discrete time asymmetric exclusion process

NASA Astrophysics Data System (ADS)

Chia, Nicholas; Bundschuh, Ralf

2005-11-01

In the universality class of the one-dimensional Kardar-Parisi-Zhang (KPZ) surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since and Derrida and Lebowitz’s original publication [Phys. Rev. Lett. 80, 209 (1998)] this universality has been verified for a variety of continuous-time, periodic-boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large-system-size limit (N→∞) of a single-particle discrete time system, even in the case of very small system sizes (N⩽22) . This fact allows us to not only verify that the DLSF properly characterizes multiple-particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open-boundary ASEP.

Macdonald index and chiral algebra

NASA Astrophysics Data System (ADS)

Song, Jaewon

2017-08-01

For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

Temperature Effect on Ionic Current and ssDNA Transport through Nanopores.

PubMed

Payet, Linda; Martinho, Marlène; Merstorf, Céline; Pastoriza-Gallego, Manuela; Pelta, Juan; Viasnoff, Virgile; Auvray, Loïc; Muthukumar, Murugappan; Mathé, Jérôme

2015-10-20

We have investigated the role of electrostatic interactions in the transport of nucleic acids and ions through nanopores. The passage of DNA through nanopores has so far been conjectured to involve a free-energy barrier for entry, followed by a downhill translocation where the driving voltage accelerates the polymer. We have tested the validity of this conjecture by using two toxins, α-hemolysin and aerolysin, which differ in their shape, size, and charge. The characteristic timescales in each toxin as a function of temperature show that the entry barrier is ∼15 kBT and the translocation barrier is ∼35 kBT, although the electrical force in the latter step is much stronger. Resolution of this fact, using a theoretical model, reveals that the attraction between DNA and the charges inside the barrel of the pore is the most dominant factor in determining the translocation speed and not merely the driving electrochemical potential gradient. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Temperature Effect on Ionic Current and ssDNA Transport through Nanopores

PubMed Central

Payet, Linda; Martinho, Marlène; Merstorf, Céline; Pastoriza-Gallego, Manuela; Pelta, Juan; Viasnoff, Virgile; Auvray, Loïc; Muthukumar, Murugappan; Mathé, Jérôme

2015-01-01

We have investigated the role of electrostatic interactions in the transport of nucleic acids and ions through nanopores. The passage of DNA through nanopores has so far been conjectured to involve a free-energy barrier for entry, followed by a downhill translocation where the driving voltage accelerates the polymer. We have tested the validity of this conjecture by using two toxins, α-hemolysin and aerolysin, which differ in their shape, size, and charge. The characteristic timescales in each toxin as a function of temperature show that the entry barrier is ∼15kBT and the translocation barrier is ∼35kBT, although the electrical force in the latter step is much stronger. Resolution of this fact, using a theoretical model, reveals that the attraction between DNA and the charges inside the barrel of the pore is the most dominant factor in determining the translocation speed and not merely the driving electrochemical potential gradient. PMID:26488651

Nanophase Nickel-Zirconium Alloys for Fuel Cells

NASA Technical Reports Server (NTRS)

Narayanan, Sekharipuram; Whitacre, jay; Valdez, Thomas

2008-01-01

Nanophase nickel-zirconium alloys have been investigated for use as electrically conductive coatings and catalyst supports in fuel cells. Heretofore, noble metals have been used because they resist corrosion in the harsh, acidic fuel cell interior environments. However, the high cost of noble metals has prompted a search for less-costly substitutes. Nickel-zirconium alloys belong to a class of base metal alloys formed from transition elements of widely different d-electron configurations. These alloys generally exhibit unique physical, chemical, and metallurgical properties that can include corrosion resistance. Inasmuch as corrosion is accelerated by free-energy differences between bulk material and grain boundaries, it was conjectured that amorphous (glassy) and nanophase forms of these alloys could offer the desired corrosion resistance. For experiments to test the conjecture, thin alloy films containing various proportions of nickel and zirconium were deposited by magnetron and radiofrequency co-sputtering of nickel and zirconium. The results of x-ray diffraction studies of the deposited films suggested that the films had a nanophase and nearly amorphous character.

Macdonald index and chiral algebra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Jaewon

For any 4dN = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. Here, we conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A 1, A 2n) and (A 1, D 2n+1) where the chiral algebras are given by Virasoro andmore » $$ˆ\\atop{su}$$(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.« less

Ion irradiation studies on the void swelling behavior of a titanium modified D9 alloy

NASA Astrophysics Data System (ADS)

Balaji, S.; Mohan, Sruthi; Amirthapandian, S.; Chinnathambi, S.; David, C.; Panigrahi, B. K.

2015-12-01

The sensitivity of Positron Annihilation Spectroscopy (PAS) for probing vacancy defects and their environment is well known. Its applicability in determination of swelling and the peak swelling temperature was put to test in our earlier work on ion irradiated D9 alloys [1]. Upon comparison with the peak swelling temperature determined by conventional step height measurements it was found that the peak swelling temperature determined using PAS was 50 K higher. It was conjectured that the positrons trapping in the irradiation induced TiC precipitation could have caused the shift. In the present work, D9 alloys have been implanted with 100 appm helium ions and subsequently implanted with 2.5 MeV Ni ions up to peak damage of 100 dpa. The nickel implantations have been carried out through a range of temperatures between 450 °C and 650 °C. The evolution of cavities and TiC precipitates at various temperatures has been followed by TEM and this report provides an experimental verification of the conjecture.

Macdonald index and chiral algebra

DOE PAGES

Song, Jaewon

2017-08-10

For any 4dN = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. Here, we conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A 1, A 2n) and (A 1, D 2n+1) where the chiral algebras are given by Virasoro andmore » $$ˆ\\atop{su}$$(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.« less

Mathematical Observations: The Genesis of Mathematical Discovery in the Classroom

ERIC Educational Resources Information Center

Beaugris, Louis M.

2013-01-01

In his "Proofs and Refutations," Lakatos identifies the "Primitive Conjecture" as the first stage in the pattern of mathematical discovery. In this article, I am interested in ways of reaching the "Primitive Conjecture" stage in an undergraduate classroom. I adapted Realistic Mathematics Education methods in an…

Matter Gravitates, but Does Gravity Matter?

ERIC Educational Resources Information Center

Groetsch, C. W.

2011-01-01

The interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giovannetti, Vittorio; Lloyd, Seth; Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Renyi entropies at the output of a channel. The conjecture is proven true for all Renyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment.

Reducing CO2 flux by decreasing tillage in Ohio: overcoming conjecture with data

USDA-ARS?s Scientific Manuscript database

Soil could become an important sink for atmospheric carbon dioxide (CO2) as global agricultural greenhouse gas emissions continue to grow, but data to support this conjecture are few. Sequestering soil carbon (C) depends upon many factors including soil type, climate, crop, tillage, nitrogen fertili...

Proof of Nishida's Conjecture on Anharmonic Lattices

NASA Astrophysics Data System (ADS)

Rink, Bob

2006-02-01

We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal computations of Nishida, the KAM theorem, discrete symmetry considerations and an algebraic trick that considerably simplifies earlier results.

The Evolution of Open Magnetic Flux Driven by Photospheric Dynamics

NASA Technical Reports Server (NTRS)

Linker, Jon A.; Lionello, Roberto; Mikic, Zoran; Titov, Viacheslav S.; Antiochos, Spiro K.

2010-01-01

The coronal magnetic field is of paramount importance in solar and heliospheric physics. Two profoundly different views of the coronal magnetic field have emerged. In quasi-steady models, the predominant source of open magnetic field is in coronal holes. In contrast, in the interchange model, the open magnetic flux is conserved, and the coronal magnetic field can only respond to the photospheric evolution via interchange reconnection. In this view the open magnetic flux diffuses through the closed, streamer belt fields, and substantial open flux is present in the streamer belt during solar minimum. However, Antiochos and co-workers, in the form of a conjecture, argued that truly isolated open flux cannot exist in a configuration with one heliospheric current sheet (HCS) - it will connect via narrow corridors to the polar coronal hole of the same polarity. This contradicts the requirements of the interchange model. We have performed an MHD simulation of the solar corona up to 20R solar to test both the interchange model and the Antiochos conjecture. We use a synoptic map for Carrington Rotation 1913 as the boundary condition for the model, with two small bipoles introduced into the region where a positive polarity extended coronal hole forms. We introduce flows at the photospheric boundary surface to see if open flux associated with the bipoles can be moved into the closed-field region. Interchange reconnection does occur in response to these motions. However, we find that the open magnetic flux cannot be simply injected into closed-field regions - the flux eventually closes down and disconnected flux is created. Flux either opens or closes, as required, to maintain topologically distinct open and closed field regions, with no indiscriminate mixing of the two. The early evolution conforms to the Antiochos conjecture in that a narrow corridor of open flux connects the portion of the coronal hole that is nearly detached by one of the bipoles. In the later evolution, a detached coronal hole forms, in apparent violation of the Antiochos conjecture. Further investigation reveals that this detached coronal hole is actually linked to the extended coronal hole by a separatrix footprint on the photosphere of zero width. Therefore, the essential idea of the conjecture is preserved, if we modify it to state that coronal holes in the same polarity region are always linked, either by finite width corridors or separatrix footprints. The implications of these results for interchange reconnection and the sources of the slow solar wind are briefly discussed.

The Evolution of Open Magnetic Flux Driven by Photospheric Dynamics

NASA Astrophysics Data System (ADS)

Linker, Jon A.; Lionello, Roberto; Mikić, Zoran; Titov, Viacheslav S.; Antiochos, Spiro K.

2011-04-01

The coronal magnetic field is of paramount importance in solar and heliospheric physics. Two profoundly different views of the coronal magnetic field have emerged. In quasi-steady models, the predominant source of open magnetic field is in coronal holes. In contrast, in the interchange model, the open magnetic flux is conserved, and the coronal magnetic field can only respond to the photospheric evolution via interchange reconnection. In this view, the open magnetic flux diffuses through the closed, streamer belt fields, and substantial open flux is present in the streamer belt during solar minimum. However, Antiochos and coworkers, in the form of a conjecture, argued that truly isolated open flux cannot exist in a configuration with one heliospheric current sheet—it will connect via narrow corridors to the polar coronal hole of the same polarity. This contradicts the requirements of the interchange model. We have performed an MHD simulation of the solar corona up to 20 R sun to test both the interchange model and the Antiochos conjecture. We use a synoptic map for Carrington rotation 1913 as the boundary condition for the model, with two small bipoles introduced into the region where a positive polarity extended coronal hole forms. We introduce flows at the photospheric boundary surface to see if open flux associated with the bipoles can be moved into the closed-field region. Interchange reconnection does occur in response to these motions. However, we find that the open magnetic flux cannot be simply injected into closed-field regions—the flux eventually closes down and disconnected flux is created. Flux either opens or closes, as required, to maintain topologically distinct open- and closed-field regions, with no indiscriminate mixing of the two. The early evolution conforms to the Antiochos conjecture in that a narrow corridor of open flux connects the portion of the coronal hole that is nearly detached by one of the bipoles. In the later evolution, a detached coronal hole forms, in apparent violation of the Antiochos conjecture. Further investigation reveals that this detached coronal hole is actually linked to the extended coronal hole by a separatrix footprint on the photosphere of zero width. Therefore, the essential idea of the conjecture is preserved, if we modify it to state that coronal holes in the same polarity region are always linked, either by finite width corridors or separatrix footprints. The implications of these results for interchange reconnection and the sources of the slow solar wind are briefly discussed.

Some constructions of biharmonic maps and Chen’s conjecture on biharmonic hypersurfaces

NASA Astrophysics Data System (ADS)

Ou, Ye-Lin

2012-04-01

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4 and 2.6), biharmonic maps between spheres (Theorem 2.9) and into spheres (Theorem 2.10) via orthogonal multiplications and eigenmaps. We also study biharmonic graphs of maps, derive the equation for a function whose graph is a biharmonic hypersurface in a Euclidean space, and give an equivalent formulation of Chen's conjecture on biharmonic hypersurfaces by using the biharmonic graph equation (Theorem 4.1) which paves a way for the analytic study of the conjecture.

An analytic study on bounds for the associated Legendre functions. [for truncation of geopotential series in spherical harmonics in orbital analyses

NASA Technical Reports Server (NTRS)

Payne, M. H.

1973-01-01

The bounds for the normalized associated Legendre functions P sub nm were studied to provide a rational basis for the truncation of the geopotential series in spherical harmonics in various orbital analyses. The conjecture is made that the largest maximum of the normalized associated Legendre function lies in the interval which indicates the greatest integer function. A procedure is developed for verifying this conjecture. An on-line algebraic manipulator, IAM, is used to implement the procedure and the verification is carried out for all n equal to or less than 2m, for m = 1 through 6. A rigorous proof of the conjecture is not available.

Dimension improvement in Dhar's refutation of the Eden conjecture

NASA Astrophysics Data System (ADS)

Bertrand, Quentin; Pertinand, Jules

2018-03-01

We consider the Eden model on the d-dimensional hypercubical unoriented lattice, for large d. Initially, every lattice point is healthy, except the origin which is infected. Then, each infected lattice point contaminates any of its neighbours with rate 1. The Eden model is equivalent to first passage percolation, with exponential passage times on edges. The Eden conjecture states that the limit shape of the Eden model is a Euclidean ball. By pushing the computations of Dhar [5] a little further with modern computers and efficient implementation we obtain improved bounds for the speed of infection. This shows that the Eden conjecture does not hold in dimension superior to 22 (the lowest known dimension was 35).

Structure of edge-state inner products in the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Fern, R.; Bondesan, R.; Simon, S. H.

2018-04-01

We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012), 10.1103/PhysRevB.86.245310]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.

Corrections to scaling for watersheds, optimal path cracks, and bridge lines

NASA Astrophysics Data System (ADS)

Fehr, E.; Schrenk, K. J.; Araújo, N. A. M.; Kadau, D.; Grassberger, P.; Andrade, J. S., Jr.; Herrmann, H. J.

2012-07-01

We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions (2D and 3D). We disclose that these models have numerically equivalent fractal dimensions and leading correction-to-scaling exponents. We conjecture all three models to possess the same fractal dimension, namely, df=1.2168±0.0005 in 2D and df=2.487±0.003 in 3D, and the same exponent of the leading correction, Ω=0.9±0.1 and Ω=1.0±0.1, respectively. The close relations between watersheds, optimal path cracks in the strong disorder limit, and bridge lines are further supported by either heuristic or exact arguments.

Entanglement of purification in free scalar field theories

NASA Astrophysics Data System (ADS)

Bhattacharyya, Arpan; Takayanagi, Tadashi; Umemoto, Koji

2018-04-01

We compute the entanglement of purification (EoP) in a 2d free scalar field theory with various masses. This quantity measures correlations between two subsystems and is reduced to the entanglement entropy when the total system is pure. We obtain explicit numerical values by assuming minimal gaussian wave functionals for the purified states. We find that when the distance between the subsystems is large, the EoP behaves like the mutual information. However, when the distance is small, the EoP shows a characteristic behavior which qualitatively agrees with the conjectured holographic computation and which is different from that of the mutual information. We also study behaviors of mutual information in purified spaces and violations of monogamy/strong superadditivity.

On the Goldbach Conjecture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friedland, G.

2018-01-08

This note confirms Goldbach’s Conjecture from 1742. This is, every even integer greater than two is the sum of two prime numbers. An analysis of the nature of multiplication as description length reduction for addition precedes a contraposition that it is impossible to subtract any prime from a given even integer without the result ever being prime.

Proof of a new colour decomposition for QCD amplitudes

DOE PAGES

Melia, Tom

2015-12-16

Recently, Johansson and Ochirov conjectured the form of a new colour decom-position for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on ‘Mario World’ Feynman diagrams, which exhibit the hierarchical Dyck structure previously found to be very useful when dealing with multi-quark amplitudes.

Weak gravity conjecture as a razor criterium for exotic D-brane instantons

NASA Astrophysics Data System (ADS)

Addazi, Andrea

2017-01-01

We discuss implications of weak gravity conjecture (WGC) for exotic D-brane instantons. In particular, WGC leads to indirect stringent bounds on non-perturbative superpotentials generated by exotic instantons with many implications for phenomenology: R-parity violating processes, neutrino mass, μ-problem, neutron-antineutron transitions and collider physics.

Developing a "Conjecturing Atmosphere" in the Classroom through Task Design and Enactment

ERIC Educational Resources Information Center

Hunter, Jodie

2014-01-01

In recent years there has been an increased emphasis on algebraic reasoning in primary school classrooms. This includes introducing students to the mathematical practices of making conjectures, justifying and generalising. Drawing on findings from a classroom-based study, this paper explores one teacher's journey in shifting her task design and…

Three Conjectures about School Effectiveness: An Exploratory Study

ERIC Educational Resources Information Center

Hofman, Roelande H.; Hofman, W. H. Adriaan; Gray, John M.

2015-01-01

In this article, we address three broad conjectures about what really matters with respect to school effectiveness. Our review of previous evidence prompted us to look at three sets of factors connected with classroom teachers, school policies and processes, and matters of governance. All three have featured prominently in the public arena. In…

Proof of a new colour decomposition for QCD amplitudes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Melia, Tom

Recently, Johansson and Ochirov conjectured the form of a new colour decom-position for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on ‘Mario World’ Feynman diagrams, which exhibit the hierarchical Dyck structure previously found to be very useful when dealing with multi-quark amplitudes.

Fostering Teacher Learning of Conjecturing, Generalising and Justifying through Mathematics Studio

ERIC Educational Resources Information Center

Lesseig, Kristin

2016-01-01

Calls to advance students' ability to engage in mathematical reasoning practices including conjecturing, generalising and justifying (CGJ) place significant new demands on teachers. This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote…

Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

ERIC Educational Resources Information Center

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

Learning Mathematics Does Not (Necessarily) Mean Constructing the Right Knowledge

ERIC Educational Resources Information Center

Dawson, Sandy

2015-01-01

In this article, which was first published in 1991, the late Sandy Dawson, discusses aspects of a Lakatosian approach to mathematics teaching. The ideas are illustrated with examples from three teaching situations: making conjectures about the next number in a sequence; making conjectures about the internal angles in a triangle using Logo; and…

Calabi's conjecture and some new results in algebraic geometry

PubMed Central

Yau, Shing-Tung

1977-01-01

We announce a proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold and then apply it to prove some new results in algebraic geometry and differential geometry. For example, we prove that the only Kähler structure on a complex projective space is the standard one. PMID:16592394

On global solutions of the random Hamilton-Jacobi equations and the KPZ problem

NASA Astrophysics Data System (ADS)

Bakhtin, Yuri; Khanin, Konstantin

2018-04-01

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing tree-like structures. We believe that the KPZ universality can be explained in terms of statistics of these structures evolving in time. The paper is focussed on the setting of the random Hamilton-Jacobi equations. We formulate several conjectures concerning global solutions and discuss how their properties are connected to the KPZ scalings in dimension 1  +  1. In the case of general viscous Hamilton-Jacobi equations with non-quadratic Hamiltonians, we define generalised directed polymers. We expect that their behaviour is similar to the behaviour of classical directed polymers, and present arguments in favour of this conjecture. We also define a new renormalisation transformation defined in purely geometrical terms and discuss conjectural properties of the corresponding fixed points. Most of our conjectures are widely open, and supported by only partial rigorous results for particular models.

A proof of Wright's conjecture

NASA Astrophysics Data System (ADS)

van den Berg, Jan Bouwe; Jaquette, Jonathan

2018-06-01

Wright's conjecture states that the origin is the global attractor for the delay differential equation y‧ (t) = - αy (t - 1) [ 1 + y (t) ] for all α ∈ (0, π/2 ] when y (t) > - 1. This has been proven to be true for a subset of parameter values α. We extend the result to the full parameter range α ∈ (0, π/2 ], and thus prove Wright's conjecture to be true. Our approach relies on a careful investigation of the neighborhood of the Hopf bifurcation occurring at α = π/2. This analysis fills the gap left by complementary work on Wright's conjecture, which covers parameter values further away from the bifurcation point. Furthermore, we show that the branch of (slowly oscillating) periodic orbits originating from this Hopf bifurcation does not have any subsequent bifurcations (and in particular no folds) for α ∈ (π/2, π/2 + 6.830 ×10-3 ]. When combined with other results, this proves that the branch of slowly oscillating solutions that originates from the Hopf bifurcation at α = π/2 is globally parametrized by α > π/2.

On stability of fixed points and chaos in fractional systems.

PubMed

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

Boundary singularities produced by the motion of soap films.

PubMed

Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I

2014-06-10

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stottmeister, Alexander, E-mail: alexander.stottmeister@gravity.fau.de; Thiemann, Thomas, E-mail: thomas.thiemann@gravity.fau.de

In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall “coherentmore » state” transform for compact Lie groups G, which we prove for G = U(1){sup n} and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ{sup 2d} are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.« less

Local Conjecturing Process in the Solving of Pattern Generalization Problem

ERIC Educational Resources Information Center

Sutarto; Nusantara, Toto; Subanji; Sisworo

2016-01-01

This aim of this study is to describe the process of local conjecturing in generalizing patterns based on Action, Process, Object, Schema (APOS) theory. The subjects were 16 grade 8 students from a junior high school. Data collection used Pattern Generalization Problem (PGP) and interviews. In the first stage, students completed PGP; in the second…

Random function theory revisited - Exact solutions versus the first order smoothing conjecture

NASA Technical Reports Server (NTRS)

Lerche, I.; Parker, E. N.

1975-01-01

We remark again that the mathematical conjecture known as first order smoothing or the quasi-linear approximation does not give the correct dependence on correlation length (time) in many cases, although it gives the correct limit as the correlation length (time) goes to zero. In this sense, then, the method is unreliable.

On the Nature of Mathematical Thought and Inquiry: A Prelusive Suggestion

ERIC Educational Resources Information Center

McLoughlin, M. Padraig M. M.

2004-01-01

The author of this paper submits that humans have a natural inquisitiveness; hence, mathematicians (as well as other humans) must be active in learning. Thus, we must commit to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning…

A master bosonization duality

NASA Astrophysics Data System (ADS)

Jensen, Kristan

2018-01-01

We conjecture a new sequence of dualities between Chern-Simons gauge theories simultaneously coupled to fundamental bosons and fermions. These dualities reduce to those proposed by Aharony when the number of bosons or fermions is zero. Our conjecture passes a number of consistency checks. These include the matching of global symmetries and consistency with level/rank duality in massive phases.

Yang-Mills theory and the ABC conjecture

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Hu, Zhi; Probst, Malte; Read, James

2018-05-01

We establish a precise correspondence between the ABC Conjecture and 𝒩 = 4 super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkies’ method of mapping ABC-triples to elliptic curves in his demonstration that ABC implies Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite brane-tiling/dimer model for a gauge theory with toric moduli space is a particular dessin d’enfant in the sense of Grothendieck. We explore this correspondence for the highest quality ABC-triples as well as large samples of random triples. The conjecture itself is mapped to a statement about the fundamental domain of the toroidal compactification of the string realization of 𝒩 = 4 SYM.

Josh's Operational Conjectures: Abductions of a Splitting Operation and the Construction of New Fractional Schemes

ERIC Educational Resources Information Center

Norton, Anderson

2008-01-01

This article reports on students' learning through conjecturing, by drawing on a semester-long teaching experiment with 6 sixth-grade students. It focuses on 1 of the students, Josh, who developed especially powerful ways of operating over the course of the teaching experiment. Through a fine-grained analysis of Josh's actions, this article…

Some recent progress in classical general relativity

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-06-01

In this short survey paper, we shall discuss certain recent results in classical gravity. Our main attention will be restricted to two topics in which we have been involved; the positive mass conjecture and its extensions to the case with horizons, including the Penrose conjecture (Part I), and the interaction of gravity with other force fields and quantum-mechanical particles (Part II).

Beyond Problem-Solving: Elementary Students' Mathematical Dispositions When Faced with the Challenge of Unsolved Problems

ERIC Educational Resources Information Center

O'Dell, Jenna R.

2017-01-01

The goal of this study was to document the characteristics of students' dispositions towards mathematics when they engaged in the exploration of parts of unsolved problems: Graceful Tree Conjecture and Collatz Conjecture. Ten students, Grades 4 and 5, from an after-school program in the Midwest participated in the study. I focused on the…

Inquiry Based Learning: A Modified Moore Method Approach To Encourage Student Research

ERIC Educational Resources Information Center

McLoughlin, M. Padraig M. M.

2008-01-01

The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method (MMM) across the…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guha, Saikat; Shapiro, Jeffrey H.; Erkmen, Baris I.

Previous work on the classical information capacities of bosonic channels has established the capacity of the single-user pure-loss channel, bounded the capacity of the single-user thermal-noise channel, and bounded the capacity region of the multiple-access channel. The latter is a multiple-user scenario in which several transmitters seek to simultaneously and independently communicate to a single receiver. We study the capacity region of the bosonic broadcast channel, in which a single transmitter seeks to simultaneously and independently communicate to two different receivers. It is known that the tightest available lower bound on the capacity of the single-user thermal-noise channel is thatmore » channel's capacity if, as conjectured, the minimum von Neumann entropy at the output of a bosonic channel with additive thermal noise occurs for coherent-state inputs. Evidence in support of this minimum output entropy conjecture has been accumulated, but a rigorous proof has not been obtained. We propose a minimum output entropy conjecture that, if proved to be correct, will establish that the capacity region of the bosonic broadcast channel equals the inner bound achieved using a coherent-state encoding and optimum detection. We provide some evidence that supports this conjecture, but again a full proof is not available.« less

Vibrational molecular modulation in hydrogen

NASA Astrophysics Data System (ADS)

Huang, Shu Wei; Chen, Wei-Jan; Kung, A. H.

2006-12-01

Detailed numerical modeling of using the vibrational coherence of H2 for molecular modulation is presented. The focus of the calculation is on a strongly driven system aimed at producing many sidebands in the presence of Doppler broadening and the effects of collisions at room temperature. It is shown that Dicke narrowing that reduces the Doppler width plays a critical role in high order sideband generation in room temperature H2 . In addition, the calculation shows that generation of many sidebands favors the phased state as has been reported in all gas phase experiments and is primarily a consequence of the Stark shifts that result from the applied high intensities. The influence of self-focusing in the gas medium that has been conjectured in previous studies is only secondary. The numerical results agree with experimental data obtained in our laboratory, where we have succeeded in generating collinearly propagating Raman sidebands with wavelengths that range from 2216nm in the infrared to 133nm in the vacuum ultraviolet. The frequencies covered by these sidebands span over four octaves for a total of more than 70600cm-1 in the optical region of the spectrum.

Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states

NASA Astrophysics Data System (ADS)

Saraceno, Marcos; Ermann, Leonardo; Cormick, Cecilia

2017-03-01

The problem of finding symmetric informationally complete positive-operator-valued-measures (SIC-POVMs) has been solved numerically for all dimensions d up to 67 [A. J. Scott and M. Grassl, J. Math. Phys. 51, 042203 (2010), 10.1063/1.3374022], but a general proof of existence is still lacking. For each dimension, it was shown that it is possible to find a SIC-POVM that is generated from a fiducial state upon application of the operators of the Heisenberg-Weyl group. We draw on the numerically determined fiducial states to study their phase-space features, as displayed by the characteristic function and the Wigner, Bargmann, and Husimi representations, adapted to a Hilbert space of finite dimension. We analyze the phase-space localization of fiducial states, and observe that the SIC-POVM condition is equivalent to a maximal delocalization property. Finally, we explore the consequences in phase space of the conjectured Zauner symmetry. In particular, we construct a Hermitian operator commuting with this symmetry that leads to a representation of fiducial states in terms of eigenfunctions with definite semiclassical features.

Three-Dimensional Analysis and Modeling of a Wankel Engine

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1991-01-01

A new computer code, AGNI-3D, has been developed for the modeling of combustion, spray, and flow properties in a stratified-charge rotary engine (SCRE). The mathematical and numerical details of the new code are described by the first author in a separate NASA publication. The solution procedure is based on an Eulerian-Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas-mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite-volume, Steger-Warming flux vector splitting scheme. The liquid-phase equations are solved in Lagrangian coordinates. The engine configuration studied was similar to existing rotary engine flow-visualization and hot-firing test rigs. The results of limited test cases indicate a good degree of qualitative agreement between the predicted and measured pressures. It is conjectured that the impulsive nature of the torque generated by the observed pressure nonuniformity may be one of the mechanisms responsible for the excessive wear of the timing gears observed during the early stages of the rotary combustion engine (RCE) development. It was identified that the turbulence intensities near top-dead-center were dominated by the compression process and only slightly influenced by the intake and exhaust processes. Slow mixing resulting from small turbulence intensities within the rotor pocket and also from a lack of formation of any significant recirculation regions within the rotor pocket were identified as the major factors leading to incomplete combustion. Detailed flowfield results during exhaust and intake, fuel injection, fuel vaporization, combustion, mixing and expansion processes are also presented. The numerical procedure is very efficient as it takes 7 to 10 CPU hours on a CRAY Y-MP for one entire engine cycle when the computations are performed over a 31 x16 x 20 grid.

Parton distributions from the nuclear physics perspective

NASA Astrophysics Data System (ADS)

Hwang, W.-Y. Pauchy

1995-05-01

In deep inelastic scattering by charged leptons, the generalized Sullivan processes, in which the virtual photon may strike and smash the meson in the cloud (or the recoiling baryon in the core), may contribute to cross sections. Recently, Hwang, Speth, and Brown have suggested that the sea quark distributions of a hadron, at low and moderate Q2 (at least up to a few GeV2), may be attributed primarily to generalized Sullivan processes. Apart from the result that the general characteristics of the various sea quark distributions, including the strengths and shapes, can be understood, the conjecture also allows for a simple interpretation of the recent finding by the New Muon Collaboration on the violation of the Gottfried sum rule [including the shape of Fp2(x)-Fn2(x) as a function of x], as well as that of the so-called ``proton spin crisis'' as caused by the observation by the European Muon Collaboration. To offer further tests of the conjecture, we mention that Drell-Yan processes and semi-inclusive Λ production may also be employed.

Leonardo da Vinci's studies of the heart.

PubMed

Shoja, Mohammadali M; Agutter, Paul S; Loukas, Marios; Benninger, Brion; Shokouhi, Ghaffar; Namdar, Husain; Ghabili, Kamyar; Khalili, Majid; Tubbs, R Shane

2013-08-20

Leonardo da Vinci's detailed drawings are justly celebrated; however, less well known are his accounts of the structures and functions of the organs. In this paper, we focus on his illustrations of the heart, his conjectures about heart and blood vessel function, his experiments on model systems to test those conjectures, and his unprecedented conclusions about the way in which the cardiovascular system operates. In particular, da Vinci seems to have been the first to recognize that the heart is a muscle and that systole is the active phase of the pump. He also seems to have understood the functions of the auricles and pulmonary veins, identified the relationship between the cardiac cycle and the pulse, and explained the hemodynamic mechanism of valve opening and closure. He also described anatomical variations and changes in structure and function that occurred with age. We outline da Vinci's varied career and suggest ways in which his personality, experience, skills and intellectual heritage contributed to these advances in understanding. We also consider his influence on later studies in anatomy and physiology. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Numerical simulations of self-focusing of ultrafast laser pulses

NASA Astrophysics Data System (ADS)

Fibich, Gadi; Ren, Weiqing; Wang, Xiao-Ping

2003-05-01

Simulation of nonlinear propagation of intense ultrafast laser pulses is a hard problem, because of the steep spatial gradients and the temporal shocks that form during the propagation. In this study we adapt the iterative grid distribution method of Ren and Wang [J. Comput. Phys. 159, 246 (2000)] to solve the two-dimensional nonlinear Schrödinger equation with normal time dispersion, space-time focusing, and self-steepening. Our simulations show that, after the asymmetric temporal pulse splitting, the rear peak self-focuses faster than the front one. As a result, the collapse of the rear peak is arrested before that of the front peak. Unlike what has sometimes been conjectured, however, collapse of the two peaks is not arrested through multiple splittings, but rather through temporal dispersion.

Leading multi-soft limits from scattering equations

NASA Astrophysics Data System (ADS)

Zlotnikov, Michael

2017-10-01

A Cachazo-He-Yuan (CHY) type formula is derived for the leading gluon, bi-adjoint scalar ϕ 3, Yang-Mills-scalar and non-linear sigma model m-soft factors S m in arbitrary dimension. The general formula is used to evaluate explicit examples for up to three soft legs analytically and up to four soft legs numerically via comparison with amplitude ratios under soft kinematics. A structural pattern for gluon m-soft factor is inferred and a simpler formula for its calculation is conjectured. In four dimensions, a Cachazo-Svrček-Witten (CSW) recursive procedure producing the leading m-soft gluon factor in spinor helicity formalism is developed as an alternative, and Britto-Cachazo-Feng-Witten (BCFW) recursion is used to obtain the leading four-soft gluon factor for all analytically distinct helicity configurations.

Fast and slow coherent cascades in anti-de Sitter spacetime

NASA Astrophysics Data System (ADS)

Dimitrakopoulos, Fotios V.; Freivogel, Ben; Pedraza, Juan F.

2018-06-01

We study the phase and amplitude dynamics of small perturbations in 3  +  1 dimensional anti-de Sitter spacetime using the truncated resonant approximation, also known as the two time framework. We analyse the phase spectrum for different classes of initial data and find that higher frequency modes turn on with coherently aligned phases. Combining numerical and analytical results, we conjecture that there is a class of initial conditions that collapse in infinite slow time and to which the well-studied case of the two-mode, equal energy initial data belongs. We additionally study perturbations that collapse in finite time, and find that the energy spectrum approaches a power law, with the energy per mode scaling approximately as the inverse first power of the frequency.

Spectral dimension and dynamics for Harper's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Michael; Austin, Elizabeth J.

1994-07-01

The spectrum of Harper's equation (a model for Bloch electrons in a magnetic field) is a fractal Cantor set if the ratio β of the area of a unit cell to that of a flux quantum is not a rational number. It has been conjectured that the second moment of an initially localized wave packet has a power-law growth of the form ~t2D0, where D0 is the box-counting dimension of the spectrum, and that D0=1/2. We present numerical results on the dimension of the spectrum and the spread of a wave packet indicating that these relationships are at best approximate. We also present heuristic arguments suggesting that there should be no general relationships between the dimension and the spread of a wave packet.

The assessment of nanofluid in a Von Karman flow with temperature relied viscosity

NASA Astrophysics Data System (ADS)

Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomrani, Ali Saleh; Malik, M. Y.

2018-06-01

This work endeavor to study the heat and mass transfer viscous nanofluid features in a Von Karman flow invoking the variable viscosity mechanism. Moreover, we have extended our study in view of heat generation and uniform suction effects. The flow triggering non-linear partial differential equations are inscribed in the non-dimensional form by manipulating suitable transformations. The resulting non-linear ordinary differential equations are solved numerically via implicit finite difference scheme in conjecture with the Newton's linearization scheme afterwards. The sought solutions are plotted graphically to present comparison between MATLAB routine bvp4c and implicit finite difference schemes. Impact of different parameters on the concentration/temperature/velocity profiles are highlighted. Further Nusselt number, skin friction and Sherwood number characteristics are discussed for better exposition.

BPS States, Torus Links and Wild Character Varieties

NASA Astrophysics Data System (ADS)

Diaconescu, Duiliu-Emanuel; Donagi, Ron; Pantev, Tony

2018-02-01

A string theoretic framework is constructed relating the cohomology of wild character varieties to refined stable pair theory and torus link invariants. Explicit conjectural formulas are derived for wild character varieties with a unique irregular point on the projective line. For this case, this leads to a conjectural colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.

The Relativistic Geometry and Dynamics of Electrons

NASA Astrophysics Data System (ADS)

Atiyah, M. F.; Malkoun, J.

2018-02-01

Atiyah and Sutcliffe (Proc R Soc Lond Ser A 458:1089-1115, 2002) made a number of conjectures about configurations of N distinct points in hyperbolic 3-space, arising from ideas of Berry and Robbins (Proc R Soc Lond Ser A 453:1771-1790, 1997). In this paper we prove all these conjectures, purely geometrically, but we also provide a physical interpretation in terms of Electrons.

Circumscribing Circumscription. A Guide to Relevance and Incompleteness,

DTIC Science & Technology

1985-10-01

other rules of conjecture, to account for resource limitations. P "- h’ MASSACHUSETTS INSTITUTE OF TECHNOLOGY ARTIFICIAL INTELLIGENCE LABORATORY A.I. Memo...of conjecture, to account for resource limitations. This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts...Institute of Technology. Support for the laboratory’s artificial intelligence research is provided in part by the Advanced Research Projects Agency

To Produce Conjectures and to Prove Them within a Dynamic Geometry Environment: A Case Study

ERIC Educational Resources Information Center

Furinghetti, Fulvia; Paola, Domingo

2003-01-01

This paper analyses a case study of a pair of students working together, who were asked to produce conjectures and to validate them within the dynamic geometry environment Cabri. Our aim is to scrutinize the students' reasoning, how the gap from perception to theory is filled, how Cabri influences the reasoning. We have singled out a sequence of…

Testing the performance of a fragment of the COI gene to identify western Palaearctic stag beetle species (Coleoptera, Lucanidae)

PubMed Central

Cox, Karen; Thomaes, Arno; Antonini, Gloria; Zilioli, Michele; De Gelas, Koen; Harvey, Deborah; Solano, Emanuela; Audisio, Paolo; McKeown, Niall; Shaw, Paul; Minetti, Robert; Bartolozzi, Luca; Mergeay, Joachim

2013-01-01

Abstract The taxonomy of stag beetles (Coleoptera: Lucanidae) remains challenging, mainly due to the sexual dimorphism and the strong allometry in males. Such conjecture confounds taxonomic based conservation efforts that are urgently needed due to numerous threats to stag beetle biodiversity. Molecular tools could help solve the problem of identification of the different recognized taxa in the “Lucanus cervus complex” and in some related Palaearctic species. We investigated the potential use of a 670 bp region at the 3’ end of the mitochondrial cytochrome c oxidase subunit I gene (COI) for barcoding purposes (different from the standard COI barcoding region). Well resolved species and subspecies were L. tetraodon, L. cervusakbesianus, L. c. laticornis, as well as the two eastern Asian outgroup taxa L. formosanus and L. hermani. Conversely, certain taxa could not be distinguished from each other based on K2P-distances and tree topologies: L. c. fabiani / L. (P.) barbarossa, L. c. judaicus / an unknown Lucanus species, L. c. cervus / L. c. turcicus / L. c. pentaphyllus / L. (P.) macrophyllus / L. ibericus. The relative roles of phenotypic plasticity, recurrent hybridisation and incomplete lineage sorting underlying taxonomic and phylogenetic discordances are discussed. PMID:24453554

Theory and experiment in gravitational physics

NASA Technical Reports Server (NTRS)

Will, C. M.

1981-01-01

New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been designed to fill a new need for a complete treatment of techniques for analyzing gravitation theory and experience. The Einstein equivalence principle and the foundations of gravitation theory are considered, taking into account the Dicke framework, basic criteria for the viability of a gravitation theory, experimental tests of the Einstein equivalence principle, Schiff's conjecture, and a model theory devised by Lightman and Lee (1973). Gravitation as a geometric phenomenon is considered along with the parametrized post-Newtonian formalism, the classical tests, tests of the strong equivalence principle, gravitational radiation as a tool for testing relativistic gravity, the binary pulsar, and cosmological tests.

Theory and experiment in gravitational physics

NASA Astrophysics Data System (ADS)

Will, C. M.

New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been designed to fill a new need for a complete treatment of techniques for analyzing gravitation theory and experience. The Einstein equivalence principle and the foundations of gravitation theory are considered, taking into account the Dicke framework, basic criteria for the viability of a gravitation theory, experimental tests of the Einstein equivalence principle, Schiff's conjecture, and a model theory devised by Lightman and Lee (1973). Gravitation as a geometric phenomenon is considered along with the parametrized post-Newtonian formalism, the classical tests, tests of the strong equivalence principle, gravitational radiation as a tool for testing relativistic gravity, the binary pulsar, and cosmological tests.

Higher dimensional Taub-NUT spaces and applications

NASA Astrophysics Data System (ADS)

Stelea, Cristian Ionut

In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden SL(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the C-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalising the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalisations of Kaluza-Klein magnetic monopoles, generalising the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalising the known Reissner-Nordstrom solutions.

Why did Einstein reject the November tensor in 1912-1913, only to come back to it in November 1915?

NASA Astrophysics Data System (ADS)

Weinstein, Galina

2018-05-01

The question of Einstein's rejection of the November tensor is re-examined in light of conflicting answers by several historians. I discuss these conflicting conjectures in view of three questions that should inform our thinking: Why did Einstein reject the November tensor in 1912, only to come back to it in 1915? Why was it hard for Einstein to recognize that the November tensor is a natural generalization of Newton's law of gravitation? Why did it take him three years to realize that the November tensor is not incompatible with Newton's law? I first briefly describe Einstein's work in the Zurich Notebook. I then discuss a number of interpretive conjectures formulated by historians and what may be inferred from them. Finally, I offer a new combined conjecture that answers the above questions.

Synchronous correlation matrices and Connes’ embedding conjecture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dykema, Kenneth J., E-mail: kdykema@math.tamu.edu; Paulsen, Vern, E-mail: vern@math.uh.edu

In the work of Paulsen et al. [J. Funct. Anal. (in press); preprint arXiv:1407.6918], the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters. In this paper, we develop these ideas further, focusing on the relations between synchronous correlation matrices and microstates. We prove that Connes’ embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices. We prove thatmore » if Connes’ embedding conjecture has a positive answer, then the tracial rank and projective rank are equal for every graph. We then apply these results to more general non-local games.« less

Jack Polynomials as Fractional Quantum Hall States and the Betti Numbers of the ( k + 1)-Equals Ideal

NASA Astrophysics Data System (ADS)

Zamaere, Christine Berkesch; Griffeth, Stephen; Sam, Steven V.

2014-08-01

We show that for Jack parameter α = -( k + 1)/( r - 1), certain Jack polynomials studied by Feigin-Jimbo-Miwa-Mukhin vanish to order r when k + 1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Motivated by the method of proof, which in the case r = 2 identifies the span of the relevant Jack polynomials with the S n -invariant part of a unitary representation of the rational Cherednik algebra, we conjecture that unitary representations of the type A Cherednik algebra have graded minimal free resolutions of Bernstein-Gelfand-Gelfand type; we prove this for the ideal of the ( k + 1)-equals arrangement in the case when the number of coordinates n is at most 2 k + 1. In general, our conjecture predicts the graded S n -equivariant Betti numbers of the ideal of the ( k + 1)-equals arrangement with no restriction on the number of ambient dimensions.

Boundary singularities produced by the motion of soap films

PubMed Central

Goldstein, Raymond E.; McTavish, James; Moffatt, H. Keith; Pesci, Adriana I.

2014-01-01

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a “neck-pinching” boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck’s geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures. PMID:24843162

Comparison of holographic and field theoretic complexities for time dependent thermofield double states

NASA Astrophysics Data System (ADS)

Yang, Run-Qiu; Niu, Chao; Zhang, Cheng-Yong; Kim, Keun-Young

2018-02-01

We compute the time-dependent complexity of the thermofield double states by four different proposals: two holographic proposals based on the "complexity-action" (CA) conjecture and "complexity-volume" (CV) conjecture, and two quantum field theoretic proposals based on the Fubini-Study metric (FS) and Finsler geometry (FG). We find that four different proposals yield both similarities and differences, which will be useful to deepen our understanding on the complexity and sharpen its definition. In particular, at early time the complexity linearly increase in the CV and FG proposals, linearly decreases in the FS proposal, and does not change in the CA proposal. In the late time limit, the CA, CV and FG proposals all show that the growth rate is 2 E/(πℏ) saturating the Lloyd's bound, while the FS proposal shows the growth rate is zero. It seems that the holographic CV conjecture and the field theoretic FG method are more correlated.

Constraints on axion inflation from the weak gravity conjecture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rudelius, Tom, E-mail: rudelius@physics.harvard.edu

2015-09-01

We derive constraints facing models of axion inflation based on decay constant alignment from a string-theoretic and quantum gravitational perspective. In particular, we investigate the prospects for alignment and 'anti-alignment' of C{sub 4} axion decay constants in type IIB string theory, deriving a strict no-go result in the latter case. We discuss the relationship of axion decay constants to the weak gravity conjecture and demonstrate agreement between our string-theoretic constraints and those coming from the 'generalized' weak gravity conjecture. Finally, we consider a particular model of decay constant alignment in which the potential of C{sub 4} axions in type IIBmore » compactifications on a Calabi-Yau three-fold is dominated by contributions from D7-branes, pointing out that this model evades some of the challenges derived earlier in our paper but is highly constrained by other geometric considerations.« less

Constraints on axion inflation from the weak gravity conjecture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rudelius, Tom

2015-09-08

We derive constraints facing models of axion inflation based on decay constant alignment from a string-theoretic and quantum gravitational perspective. In particular, we investigate the prospects for alignment and ‘anti-alignment’ of C{sub 4} axion decay constants in type IIB string theory, deriving a strict no-go result in the latter case. We discuss the relationship of axion decay constants to the weak gravity conjecture and demonstrate agreement between our string-theoretic constraints and those coming from the ‘generalized’ weak gravity conjecture. Finally, we consider a particular model of decay constant alignment in which the potential of C{sub 4} axions in type IIBmore » compactifications on a Calabi-Yau three-fold is dominated by contributions from D7-branes, pointing out that this model evades some of the challenges derived earlier in our paper but is highly constrained by other geometric considerations.« less

Hoop conjecture for colliding black holes

NASA Astrophysics Data System (ADS)

Ida, Daisuke; Nakao, Ken-Ichi; Siino, Masaru; Hayward, Sean A.

1998-12-01

We study the collision of black holes in the Kastor-Traschen space-time, at present the only such analytic solution. We investigate the dynamics of the event horizon in the case of the collision of two equal black holes, using the ray-tracing method. We confirm that the event horizon has trouser topology and show that its set of past end points (where the horizon is nonsmooth) is a spacelike curve resembling a seam of trousers. We show that this seam has a finite length and argue that twice this length be taken to define the minimal circumference C of the event horizon. Comparing with the asymptotic mass M, we find the inequality C<4πM supposed by the hoop conjecture, with both sides being of similar order, C~4πM. This supports the hoop conjecture as a guide to general gravitational collapse, even in the extreme case of head-on black-hole collisions.

Conjecturing via analogical reasoning constructs ordinary students into like gifted student

NASA Astrophysics Data System (ADS)

Supratman; Ratnaningsih, N.; Ryane, S.

2017-12-01

The purpose of this study is to reveal the development of knowledge of ordinary students to be like gifted students in the classroom based on Piaget's theory. In exposing it, students are given an open problem of classical analogy. Researchers explore students who conjecture via analogical reasoning in problem solving. Of the 32 students, through the method of think out loud and the interview was completed: 25 students conjecture via analogical reasoning. Of the 25 students, all of them have almost the same character in problem solving/knowledge construction. For that, a student is taken to analyze the thinking process while solving the problem/construction of knowledge based on Piaget's theory. Based on Piaget's theory in the development of the same knowledge, gifted students and ordinary students have similar structures in final equilibrium. They begin processing: assimilation and accommodation of problem, strategies, and relationships.

Empirical tests of Zipf's law mechanism in open source Linux distribution.

PubMed

Maillart, T; Sornette, D; Spaeth, S; von Krogh, G

2008-11-21

Zipf's power law is a ubiquitous empirical regularity found in many systems, thought to result from proportional growth. Here, we establish empirically the usually assumed ingredients of stochastic growth models that have been previously conjectured to be at the origin of Zipf's law. We use exceptionally detailed data on the evolution of open source software projects in Linux distributions, which offer a remarkable example of a growing complex self-organizing adaptive system, exhibiting Zipf's law over four full decades.

Rotating Black Holes and the Kerr Metric

NASA Astrophysics Data System (ADS)

Kerr, Roy Patrick

2008-10-01

Since it was first discovered in 1963 the Kerr metric has been used by relativists as a test-bed for conjectures on worm-holes, time travel, closed time-like loops, and the existence or otherwise of global Cauchy surfaces. More importantly, it has also used by astrophysicists to investigate the effects of collapsed objects on their local environments. These two groups of applications should not be confused. Astrophysical Black Holes are not the same as the Kruskal solution and its generalisations.

Supersymmetric Casimir energy and the anomaly polynomial

NASA Astrophysics Data System (ADS)

Bobev, Nikolay; Bullimore, Mathew; Kim, Hee-Cheol

2015-09-01

We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology S 1 × S D-1 is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.

Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model

NASA Astrophysics Data System (ADS)

Xun, Zhi-Peng; Tang, Gang; Han, Kui; Hao, Da-Peng; Xia, Hui; Zhou, Wei; Yang, Xi-Quan; Wen, Rong-Ji; Chen, Yu-Ling

2010-07-01

In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L > 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.

Evolution and End Point of the Black String Instability: Large D Solution.

PubMed

Emparan, Roberto; Suzuki, Ryotaku; Tanabe, Kentaro

2015-08-28

We derive a simple set of nonlinear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable nonuniform black strings. This proves an earlier conjecture about the end point of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly nonuniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the nonlinear dynamics of anti-de Sitter black branes at large D.

Simulations of Turbine Cooling Flows Using a Multiblock-Multigrid Scheme

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Ameri, Ali A.; Rigby, David L.

1996-01-01

Results from numerical simulations of air flow and heat transfer in a 'branched duct' geometry are presented. The geometry contains features, including pins and a partition, as are found in coolant passages of turbine blades. The simulations were performed using a multi-block structured grid system and a finite volume discretization of the governing equations (the compressible Navier-Stokes equations). The effects of turbulence on the mean flow and heat transfer were modeled using the Baldwin-Lomax turbulence model. The computed results are compared to experimental data. It was found that the extent of some regions of high heat transfer was somewhat under predicted. It is conjectured that the underlying reason is the local nature of the turbulence model which cannot account for upstream influence on the turbulence field. In general, however, the comparison with the experimental data is favorable.

Belief Propagation Algorithm for Portfolio Optimization Problems

PubMed Central

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462

Self-organization of cosmic radiation pressure instability. II - One-dimensional simulations

NASA Technical Reports Server (NTRS)

Hogan, Craig J.; Woods, Jorden

1992-01-01

The clustering of statistically uniform discrete absorbing particles moving solely under the influence of radiation pressure from uniformly distributed emitters is studied in a simple one-dimensional model. Radiation pressure tends to amplify statistical clustering in the absorbers; the absorbing material is swept into empty bubbles, the biggest bubbles grow bigger almost as they would in a uniform medium, and the smaller ones get crushed and disappear. Numerical simulations of a one-dimensional system are used to support the conjecture that the system is self-organizing. Simple statistics indicate that a wide range of initial conditions produce structure approaching the same self-similar statistical distribution, whose scaling properties follow those of the attractor solution for an isolated bubble. The importance of the process for large-scale structuring of the interstellar medium is briefly discussed.

Dynamical analysis of continuous higher-order hopfield networks for combinatorial optimization.

PubMed

Atencia, Miguel; Joya, Gonzalo; Sandoval, Francisco

2005-08-01

In this letter, the ability of higher-order Hopfield networks to solve combinatorial optimization problems is assessed by means of a rigorous analysis of their properties. The stability of the continuous network is almost completely clarified: (1) hyperbolic interior equilibria, which are unfeasible, are unstable; (2) the state cannot escape from the unitary hypercube; and (3) a Lyapunov function exists. Numerical methods used to implement the continuous equation on a computer should be designed with the aim of preserving these favorable properties. The case of nonhyperbolic fixed points, which occur when the Hessian of the target function is the null matrix, requires further study. We prove that these nonhyperbolic interior fixed points are unstable in networks with three neurons and order two. The conjecture that interior equilibria are unstable in the general case is left open.

Scaling properties of multiscale equilibration

NASA Astrophysics Data System (ADS)

Detmold, W.; Endres, M. G.

2018-04-01

We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale. Focusing on nontopological long-distance observables in pure S U (3 ) gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing. Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.

Belief Propagation Algorithm for Portfolio Optimization Problems.

PubMed

Shinzato, Takashi; Yasuda, Muneki

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

Tomography and generative training with quantum Boltzmann machines

NASA Astrophysics Data System (ADS)

Kieferová, Mária; Wiebe, Nathan

2017-12-01

The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless BQP=BPP , provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.

The relationship between stochastic and deterministic quasi-steady state approximations.

PubMed

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R

2015-11-23

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Numerical simulation code for self-gravitating Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Madarassy, Enikő J. M.; Toth, Viktor T.

2013-04-01

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson’s equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 109 years using a finer (100×100×100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Catalogue identifier: AEOR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOR_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5248 No. of bytes in distributed program, including test data, etc.: 715402 Distribution format: tar.gz Programming language: C++ or FORTRAN. Computer: PCs or workstations. Operating system: Linux or Windows. Classification: 1.5. Nature of problem: Simulation of a self-gravitating Bose-Einstein condensate by simultaneous solution of the Gross-Pitaevskii and Poisson equations in three dimensions. Solution method: The Gross-Pitaevskii equation is solved numerically using the Crank-Nicholson method; Poisson’s equation is solved using the relaxation method. The time evolution of the system is governed by the Gross-Pitaevskii equation; the solution of Poisson’s equation at each time step is used as an initial estimate for the next time step, which dramatically increases the efficiency of the relaxation method. Running time: Depends on the chosen size of the problem. On a typical personal computer, a 100×100×100 grid can be solved with a time span of 10 Gyr in approx. a day of running time.

Investigation on the effect of diaphragm on the combustion characteristics of solid-fuel ramjet

NASA Astrophysics Data System (ADS)

Gong, Lunkun; Chen, Xiong; Yang, Haitao; Li, Weixuan; Zhou, Changsheng

2017-10-01

The flow field characteristics and the regression rate distribution of solid-fuel ramjet with three-hole diaphragm were investigated by numerical and experimental methods. The experimental data were obtained by burning high-density polyethylene using a connected-pipe facility to validate the numerical model and analyze the combustion efficiency of the solid-fuel ramjet. The three-dimensional code developed in the present study adopted three-order MUSCL and central difference schemes, AUSMPW + flux vector splitting method, and second-order moment turbulence-chemistry model, together with k-ω shear stress transport (SST) turbulence model. The solid fuel surface temperature was calculated with fluid-solid heat coupling method. The numerical results show that strong circumferential flow exists in the region upstream of the diaphragm. The diaphragm can enhance the regression rate of the solid fuel in the region downstream of the diaphragm significantly, which mainly results from the increase of turbulent viscosity. As the diaphragm port area decreases, the regression rate of the solid fuel downstream of the diaphragm increases. The diaphragm can result in more sufficient mixing between the incoming air and fuel pyrolysis gases, while inevitably producing some pressure loss. The experimental results indicate that the effect of the diaphragm on the combustion efficiency of hydrocarbon fuels is slightly negative. It is conjectured that the diaphragm may have some positive effects on the combustion efficiency of the solid fuel with metal particles.

Cluster Adjacency Properties of Scattering Amplitudes in N =4 Supersymmetric Yang-Mills Theory

NASA Astrophysics Data System (ADS)

Drummond, James; Foster, Jack; Gürdoǧan, Ömer

2018-04-01

We conjecture a new set of analytic relations for scattering amplitudes in planar N =4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr (4 ,n ). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.

Super-light baryo-photons, weak gravity conjecture and exotic instantons in neutron-antineutron transitions

NASA Astrophysics Data System (ADS)

Addazi, Andrea

2018-05-01

In companion papers (A. Addazi, Nuovo Cim. C, 38(1): 21 (2015); A. Addazi, Z. Berezhiani, and Y. Kamyshkov, arXiv:1607.00348), we have discussed current bounds on a new super-light baryo-photon, associated with a U(1) B-L gauge, from current neutron-antineutron data, which are competitive with Eötvös-type experiments. Here, we discuss the implications of possible baryo-photon detection in string theory and quantum gravity. The discovery of a very light gauge boson should imply violation of the weak gravity conjecture, carrying deep consequences for our understanding of holography, quantum gravity and black holes. We also show how the detection of a baryo-photon would exclude the generation of all B–L violating operators from exotic stringy instantons. We will argue against the common statement in the literature that neutron-antineutron data may indirectly test at least the 300–1000 TeV scale. Searches for baryo-photons can provide indirect information on the Planck (or string) scale (quantum black holes, holography and non-perturbative stringy effects). This strongly motivates new neutron-antineutron experiments with adjustable magnetic fields dedicated to the detection of super-light baryo-photons.

Numerical Determination of Critical Conditions for Thermal Ignition

NASA Technical Reports Server (NTRS)

Luo, W.; Wake, G. C.; Hawk, C. W.; Litchford, R. J.

2008-01-01

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

On the relevance of droplet sedimentation in stratocumulus-top mixing

NASA Astrophysics Data System (ADS)

Mellado, Juan Pedro; de Lozar, Alberto

2017-11-01

The interaction between droplet sedimentation, turbulent mixing, evaporative cooling, and radiative cooling at the top of stratocumulus clouds has been studied using direct numerical simulations. This interaction is important to determine the mixing rate of the cloud and dry air above it, which eventually determines the cloud lifetime. By investigating the entrainment-rate equation, which is an analytical relationship between the contributions to cloud-top entrainment from the phenomena indicated above, we have found that the reduction of entrainment velocity by droplet sedimentation can be 2 to 3 times larger than previously conjectured. The reason is twofold. First, the reduction of evaporative cooling as droplets fall out of the inversion is stronger than previously observed in large-eddy simulations, where excessive mixing by turbulence models and numerical artifacts may have partially masked this effect of sedimentation on entrainment. Second, there is a non-negligible direct contribution from mass loading, as falling droplets leave behind more buoyant air in the inversion. This contribution is proportional to the fifth moment of the droplet-size distribution, which provides further evidence for the need to better understand the evolution of the droplet-size distribution.

Existence of Corotating and Counter-Rotating Vortex Pairs for Active Scalar Equations

NASA Astrophysics Data System (ADS)

Hmidi, Taoufik; Mateu, Joan

2017-03-01

In this paper, we study the existence of corotating and counter-rotating pairs of simply connected patches for Euler equations and the {(SQG)_{α}} equations with {α in (0,1)}. From the numerical experiments implemented for Euler equations in Deem and Zabusky (Phys Rev Lett 40(13):859-862, 1978), Pierrehumbert (J Fluid Mech 99:129-144, 1980), Saffman and Szeto (Phys Fluids 23(12):2339-2342, 1980) it is conjectured the existence of a curve of steady vortex pairs passing through the point vortex pairs. There are some analytical proofs based on variational principle (Keady in J Aust Math Soc Ser B 26:487-502, 1985; Turkington in Nonlinear Anal Theory Methods Appl 9(4):351-369, 1985); however, they do not give enough information about the pairs, such as the uniqueness or the topological structure of each single vortex. We intend in this paper to give direct proofs confirming the numerical experiments and extend these results for the {(SQG)_{α}} equation when {α in (0,1)}. The proofs rely on the contour dynamics equations combined with a desingularization of the point vortex pairs and the application of the implicit function theorem.

The Feigin Tetrahedron

NASA Astrophysics Data System (ADS)

Rupel, Dylan

2015-03-01

The first goal of this note is to extend the well-known Feigin homomorphisms taking quantum groups to quantum polynomial algebras. More precisely, we define generalized Feigin homomorphisms from a quantum shuffle algebra to quantum polynomial algebras which extend the classical Feigin homomorphisms along the embedding of the quantum group into said quantum shuffle algebra. In a recent work of Berenstein and the author, analogous extensions of Feigin homomorphisms from the dual Hall-Ringel algebra of a valued quiver to quantum polynomial algebras were defined. To relate these constructions, we establish a homomorphism, dubbed the quantum shuffle character, from the dual Hall-Ringel algebra to the quantum shuffle algebra which relates the generalized Feigin homomorphisms. These constructions can be compactly described by a commuting tetrahedron of maps beginning with the quantum group and terminating in a quantum polynomial algebra. The second goal in this project is to better understand the dual canonical basis conjecture for skew-symmetrizable quantum cluster algebras. In the symmetrizable types it is known that dual canonical basis elements need not have positive multiplicative structure constants, while this is still suspected to hold for skew-symmetrizable quantum cluster algebras. We propose an alternate conjecture for the symmetrizable types: the cluster monomials should correspond to irreducible characters of a KLR algebra. Indeed, the main conjecture of this note would establish this ''KLR conjecture'' for acyclic skew-symmetrizable quantum cluster algebras: that is, we conjecture that the images of rigid representations under the quantum shuffle character give irreducible characters for KLR algebras. We sketch a proof in the symmetric case giving an alternative to the proof of Kimura-Qin that all non-initial cluster variables in an acyclic skew-symmetric quantum cluster algebra are contained in the dual canonical basis. With these results in mind we interpret the cluster mutations directly in terms of the representation theory of the KLR algebra.

The effects of demand uncertainty on strategic gaming in the merit-order electricity pool market

NASA Astrophysics Data System (ADS)

Frem, Bassam

In a merit-order electricity pool market, generating companies (Gencos) game with their offered incremental cost to meet the electricity demand and earn bigger market shares and higher profits. However when the demand is treated as a random variable instead of as a known constant, these Genco gaming strategies become more complex. After a brief introduction of electricity markets and gaming, the effects of demand uncertainty on strategic gaming are studied in two parts: (1) Demand modelled as a discrete random variable (2) Demand modelled as a continuous random variable. In the first part, we proposed an algorithm, the discrete stochastic strategy (DSS) algorithm that generates a strategic set of offers from the perspective of the Gencos' profits. The DSS offers were tested and compared to the deterministic Nash equilibrium (NE) offers based on the predicted demand. This comparison, based on the expected Genco profits, showed the DSS to be a better strategy in a probabilistic sense than the deterministic NE. In the second part, we presented three gaming strategies: (1) Deterministic NE (2) No-Risk (3) Risk-Taking. The strategies were then tested and their profit performances were compared using two assessment tools: (a) Expected value and standard deviation (b) Inverse cumulative distribution. We concluded that despite yielding higher profit performance under the right conjectures, Risk-Taking strategies are very sensitive to incorrect conjectures on the competitors' gaming decisions. As such, despite its lower profit performance, the No-Risk strategy was deemed preferable.

Optimal time travel in the Gödel universe

NASA Astrophysics Data System (ADS)

Natário, José

2012-04-01

Using the theory of optimal rocket trajectories in general relativity, recently developed in Henriques and Natário (2011), we present a candidate for the minimum total integrated acceleration closed timelike curve in the Gödel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament's conjectured value (Malament 1984), as was already implicit in the work of Manchak (Gen. Relativ. Gravit. 51-60, 2011); however, Malament's conjecture does seem to hold for periodic closed timelike curves.

Foundations for a theory of gravitation theories

NASA Technical Reports Server (NTRS)

Thorne, K. S.; Lee, D. L.; Lightman, A. P.

1972-01-01

A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (1) a glossary of fundamental concepts; (2) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (3) a conjecture (due to Schiff) that the Weak Equivalence Principle implies the Einstein Equivalence Principle; and (4) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.

On axionic field ranges, loopholes and the weak gravity conjecture

DOE PAGES

Brown, Jon; Cottrell, William; Shiu, Gary; ...

2016-04-05

Here, we clarify some aspects of the impact that the Weak Gravity Conjecture has on models of (generalized) natural inflation. In particular we address certain technical and conceptual concerns recently raised regarding the stringent constraints and conclusions found in our previous work. We also point out the difficulties faced by attempts to evade these constraints. Furthermore, these new considerations improve the understanding of the quantum gravity constraints we found and further support the conclusion that it remains challenging for axions to drive natural inflation.

Modeling shock waves in an ideal gas: combining the Burnett approximation and Holian's conjecture.

PubMed

He, Yi-Guang; Tang, Xiu-Zhang; Pu, Yi-Kang

2008-07-01

We model a shock wave in an ideal gas by combining the Burnett approximation and Holian's conjecture. We use the temperature in the direction of shock propagation rather than the average temperature in the Burnett transport coefficients. The shock wave profiles and shock thickness are compared with other theories. The results are found to agree better with the nonequilibrium molecular dynamics (NEMD) and direct simulation Monte Carlo (DSMC) data than the Burnett equations and the modified Navier-Stokes theory.

Long-time predictability in disordered spin systems following a deep quench

NASA Astrophysics Data System (ADS)

Ye, J.; Gheissari, R.; Machta, J.; Newman, C. M.; Stein, D. L.

2017-04-01

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit—in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

Long-time predictability in disordered spin systems following a deep quench.

PubMed

Ye, J; Gheissari, R; Machta, J; Newman, C M; Stein, D L

2017-04-01

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit-in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph

NASA Astrophysics Data System (ADS)

Noja, Diego; Pelinovsky, Dmitry; Shaikhova, Gaukhar

2015-07-01

We develop a detailed analysis of edge bifurcations of standing waves in the nonlinear Schrödinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the junction). It is shown in the recent work [7] by using explicit Jacobi elliptic functions that the cubic NLS equation on a tadpole graph admits a rich structure of standing waves. Among these, there are different branches of localized waves bifurcating from the edge of the essential spectrum of an associated Schrödinger operator. We show by using a modified Lyapunov-Schmidt reduction method that the bifurcation of localized standing waves occurs for every positive power nonlinearity. We distinguish a primary branch of never vanishing standing waves bifurcating from the trivial solution and an infinite sequence of higher branches with oscillating behavior in the ring. The higher branches bifurcate from the branches of degenerate standing waves with vanishing tail outside the ring. Moreover, we analyze stability of bifurcating standing waves. Namely, we show that the primary branch is composed by orbitally stable standing waves for subcritical power nonlinearities, while all nontrivial higher branches are linearly unstable near the bifurcation point. The stability character of the degenerate branches remains inconclusive at the analytical level, whereas heuristic arguments based on analysis of embedded eigenvalues of negative Krein signatures support the conjecture of their linear instability at least near the bifurcation point. Numerical results for the cubic NLS equation show that this conjecture is valid and that the degenerate branches become spectrally stable far away from the bifurcation point.

Does a Single Eigenstate Encode the Full Hamiltonian?

NASA Astrophysics Data System (ADS)

Garrison, James R.; Grover, Tarun

2018-04-01

The eigenstate thermalization hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: For which class of operators, local or nonlocal, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: Is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where, in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities (or temperatures) using just a single eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a nonintegrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and we find that, even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of all operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle-number conserving model at infinite temperature that substantiates our conjectures.

The thermoelastic Aldo contact model with frictional heating

NASA Astrophysics Data System (ADS)

Afferrante, L.; Ciavarella, M.

2004-03-01

In the study of the essential features of thermoelastic contact, Comninou and Dundurs (J. Therm. Stresses 3 (1980) 427) devised a simplified model, the so-called "Aldo model", where the full 3 D body is replaced by a large number of thin rods normal to the interface and insulated between each other, and the system was further reduced to 2 rods by Barber's Conjecture (ASME J. Appl. Mech. 48 (1981) 555). They studied in particular the case of heat flux at the interface driven by temperature differences of the bodies, and opposed by a contact resistance, finding possible multiple and history dependent solutions, depending on the imposed temperature differences. The Aldo model is here extended to include the presence of frictional heating. It is found that the number of solutions of the problem is still always odd, and Barber's graphical construction and the stability analysis of the previous case with no frictional heating can be extended. For any given imposed temperature difference, a critical speed is found for which the uniform pressure solution becomes non-unique and/or unstable. For one direction of the temperature difference, the uniform pressure solution is non-unique before it becomes unstable. When multiple solutions occur, outermost solutions (those involving only one rod in contact) are always stable. A full numerical analysis has been performed to explore the transient behaviour of the system, in the case of two rods of different size. In the general case of N rods, Barber's conjecture is shown to hold since there can only be two stable states for all the rods, and the reduction to two rods is always possible, a posteriori.

Index formulas for higher order Loewner vector fields

NASA Astrophysics Data System (ADS)

Broad, Steven

Let ∂ be the Cauchy-Riemann operator and f be a C real-valued function in a neighborhood of 0 in R in which ∂z¯nf≠0 for all z≠0. In such cases, ∂z¯nf is known as a Loewner vector field due to its connection with Loewner's conjecture that the index of such a vector field is bounded above by n. The n=2 case of Loewner's conjecture implies Carathéodory's conjecture that any C-immersion of S into R must have at least two umbilics. Recent work of F. Xavier produced a formula for computing the index of Loewner vector fields when n=2 using data about the Hessian of f. In this paper, we extend this result and establish an index formula for ∂z¯nf for all n⩾2. Structurally, our index formula provides a defect term, which contains geometric data extracted from Hessian-like objects associated with higher order derivatives of f.

Hypnagogic and hypnopompic hallucinations during sleep paralysis: neurological and cultural construction of the night-mare.

PubMed

Cheyne, J A; Rueffer, S D; Newby-Clark, I R

1999-09-01

Hypnagogic and hypnopompic experiences (HHEs) accompanying sleep paralysis (SP) are often cited as sources of accounts of supernatural nocturnal assaults and paranormal experiences. Descriptions of such experiences are remarkably consistent across time and cultures and consistent also with known mechanisms of REM states. A three-factor structural model of HHEs based on their relations both to cultural narratives and REM neurophysiology is developed and tested with several large samples. One factor, labeled Intruder, consisting of sensed presence, fear, and auditory and visual hallucinations, is conjectured to originate in a hypervigilant state initiated in the midbrain. Another factor, Incubus, comprising pressure on the chest, breathing difficulties, and pain, is attributed to effects of hyperpolarization of motoneurons on perceptions of respiration. These two factors have in common an implied alien "other" consistent with occult narratives identified in numerous contemporary and historical cultures. A third factor, labeled Unusual Bodily Experiences, consisting of floating/flying sensations, out-of-body experiences, and feelings of bliss, is related to physically impossible experiences generated by conflicts of endogenous and exogenous activation related to body position, orientation, and movement. Implications of this last factor for understanding of orientational primacy in self-consciousness are considered. Central features of the model developed here are consistent with recent work on hallucinations associated with hypnosis and schizophrenia. Copyright 1999 Academic Press.

Shape dependence of holographic Rényi entropy in general dimensions

DOE PAGES

Bianchi, Lorenzo; Chapman, Shira; Dong, Xi; ...

2016-11-29

We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove amore » set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.« less

Quantitative evaluation of first-order retardation corrections to the quarkonium spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brambilla, N.; Prosperi, G.M.

1992-08-01

We evaluate numerically first-order retardation corrections for some charmonium and bottomonium masses under the usual assumption of a Bethe-Salpeter purely scalar confinement kernel. The result depends strictly on the use of an additional effective potential to express the corrections (rather than to resort to Kato perturbation theory) and on an appropriate regularization prescription. The kernel has been chosen in order to reproduce in the instantaneous approximation a semirelativistic potential suggested by the Wilson loop method. The calculations are performed for two sets of parameters determined by fits in potential theory. The corrections turn out to be typically of the ordermore » of a few hundred MeV and depend on an additional scale parameter introduced in the regularization. A conjecture existing in the literature on the origin of the constant term in the potential is also discussed.« less

Non-perturbative String Theory from Water Waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iyer, Ramakrishnan; Johnson, Clifford V.; /Southern California U.

2012-06-14

We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theoriesmore » coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.« less

Shear-induced inflation of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Klimchuk, James A.

1989-01-01

Using numerical models of force-free magnetic fields, the shearing of footprints in arcade geometries leading to an inflation of the coronal magnetic field was examined. For each of the shear profiles considered, all of the field lines become elevated compared with the potential field. This includes cases where the shear is concentrated well away from the arcade axis, such that B(sub z), the component of field parallel to the axis, increases outward to produce an inward B(sub z)squared/8 pi magnetic pressure gradient force. These results contrast with an earlier claim, shown to be incorrect, that field lines can sometimes become depressed as a result of shear. It is conjectured that an inflation of the entire field will always result from the shearing of simple arcade configurations. These results have implications for prominence formation, the interplanetary magnetic flux, and possibly also coronal holes.

Shear-induced inflation of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Klimchuk, James A.

1990-01-01

Using numerical models of force-free magnetic fields, the shearing of footprints in arcade geometries leading to an inflation of the coronal magnetic field was examined. For each of the shear profiles considered, all of the field lines become elevated compared with the potential field. This includes cases where the shear is concentrated well away from the arcade axis, such that B(sub z), the component of field parallel to the axis, increases outward to produce an inward B(sub z) squared/8 pi magnetic pressure gradient force. These results contrast with an earlier claim, shown to be incorrect, that field lines can sometimes become depressed as a result of shear. It is conjectured that an inflation of the entire field will always result from the shearing of simple arcade configurations. These results have implications for prominence formation, the interplanetary magnetic flux, and possibly also coronal holes.

Spectral partitioning in equitable graphs.

PubMed

Barucca, Paolo

2017-06-01

Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.

Spikelets in Pyramidal Neurons: Action Potentials Initiated in the Axon Initial Segment That Do Not Activate the Soma.

PubMed

Michalikova, Martina; Remme, Michiel W H; Kempter, Richard

2017-01-01

Spikelets are small spike-like depolarizations that can be measured in somatic intracellular recordings. Their origin in pyramidal neurons remains controversial. To explain spikelet generation, we propose a novel single-cell mechanism: somato-dendritic input generates action potentials at the axon initial segment that may fail to activate the soma and manifest as somatic spikelets. Using mathematical analysis and numerical simulations of compartmental neuron models, we identified four key factors controlling spikelet generation: (1) difference in firing threshold, (2) impedance mismatch, and (3) electrotonic separation between the soma and the axon initial segment, as well as (4) input amplitude. Because spikelets involve forward propagation of action potentials along the axon while they avoid full depolarization of the somato-dendritic compartments, we conjecture that this mode of operation saves energy and regulates dendritic plasticity while still allowing for a read-out of results of neuronal computations.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions.

PubMed

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-04-22

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions

PubMed Central

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-01-01

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems. PMID:27102945

On the optimal use of a slow server in two-stage queueing systems

NASA Astrophysics Data System (ADS)

Papachristos, Ioannis; Pandelis, Dimitrios G.

2017-07-01

We consider two-stage tandem queueing systems with a dedicated server in each queue and a slower flexible server that can attend both queues. We assume Poisson arrivals and exponential service times, and linear holding costs for jobs present in the system. We study the optimal dynamic assignment of servers to jobs assuming that two servers cannot collaborate to work on the same job and preemptions are not allowed. We formulate the problem as a Markov decision process and derive properties of the optimal allocation for the dedicated (fast) servers. Specifically, we show that the one downstream should not idle, and the same is true for the one upstream when holding costs are larger there. The optimal allocation of the slow server is investigated through extensive numerical experiments that lead to conjectures on the structure of the optimal policy.

Sea-quark distributions in the pion

NASA Astrophysics Data System (ADS)

Hwang, W.-Y. P.; Speth, J.

1992-05-01

Using Sullivan processes with ρππ, K*+K¯ 0π, and K¯ *0K+π vertices, we describe how the sea-quark distributions of a pion may be generated in a quantitative manner. The input valence-quark distributions are obtained using the leading Fock component of the light-cone wave function, which is in accord with results obtained from the QCD sum rules. The sample numerical results appear to be reasonable as far as the existing Drell-Yan production data are concerned, although the distributions as a function of x differs slightly from those obtained by imposing counting rules for x-->0 and x-->1. Our results lend additional support toward the conjecture of Hwang, Speth, and Brown that the sea distributions of a hadron, at low and moderate Q2 (at least up to a few GeV2), may be attributed primarily to generalized Sullivan processes.

Spectral partitioning in equitable graphs

NASA Astrophysics Data System (ADS)

Barucca, Paolo

2017-06-01

Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.

Long-Range Correlation in alpha-Wave Predominant EEG in Human

NASA Astrophysics Data System (ADS)

Sharif, Asif; Chyan Lin, Der; Kwan, Hon; Borette, D. S.

2004-03-01

The background noise in the alpha-predominant EEG taken from eyes-open and eyes-closed neurophysiological states is studied. Scale-free characteristic is found in both cases using the wavelet approach developed by Simonsen and Nes [1]. The numerical results further show the scaling exponent during eyes-closed is consistently lower than eyes-open. We conjecture the origin of this difference is related to the temporal reconfiguration of the neural network in the brain. To further investigate the scaling structure of the EEG background noise, we extended the second order statistics to higher order moments using the EEG increment process. We found that the background fluctuation in the alpha-predominant EEG is predominantly monofractal. Preliminary results are given to support this finding and its implication in brain functioning is discussed. [1] A.H. Simonsen and O.M. Nes, Physical Review E, 58, 2779¡V2748 (1998).

Dynamics of marginally trapped surfaces in a binary black hole merger: Growth and approach to equilibrium

NASA Astrophysics Data System (ADS)

Gupta, Anshu; Krishnan, Badri; Nielsen, Alex B.; Schnetter, Erik

2018-04-01

The behavior of quasilocal black hole horizons in a binary black hole merger is studied numerically. We compute the horizon multipole moments, fluxes, and other quantities on black hole horizons throughout the merger. These lead to a better qualitative and quantitative understanding of the coalescence of two black holes: how the final black hole is formed, initially grows, and then settles down to a Kerr black hole. We calculate the rate at which the final black hole approaches equilibrium in a fully nonperturbative situation and identify a time at which the linear ringdown phase begins. Finally, we provide additional support for the conjecture that fields at the horizon are correlated with fields in the wave zone by comparing the in-falling gravitational wave flux at the horizon to the outgoing flux as estimated from the gravitational waveform.

The impact of fraction magnitude knowledge on algebra performance and learning.

PubMed

Booth, Julie L; Newton, Kristie J; Twiss-Garrity, Laura K

2014-02-01

Knowledge of fractions is thought to be crucial for success with algebra, but empirical evidence supporting this conjecture is just beginning to emerge. In the current study, Algebra 1 students completed magnitude estimation tasks on three scales (0-1 [fractions], 0-1,000,000, and 0-62,571) just before beginning their unit on equation solving. Results indicated that fraction magnitude knowledge, and not whole number knowledge, was especially related to students' pretest knowledge of equation solving and encoding of equation features. Pretest fraction knowledge was also predictive of students' improvement in equation solving and equation encoding skills. Students' placement of unit fractions (e.g., those with a numerator of 1) was not especially useful for predicting algebra performance and learning in this population. Placement of non-unit fractions was more predictive, suggesting that proportional reasoning skills might be an important link between fraction knowledge and learning algebra. Copyright © 2013 Elsevier Inc. All rights reserved.

a Speculative Study on Negative-Dimensional Potential and Wave Problems by Implicit Calculus Modeling Approach

NASA Astrophysics Data System (ADS)

Chen, Wen; Wang, Fajie

Based on the implicit calculus equation modeling approach, this paper proposes a speculative concept of the potential and wave operators on negative dimensionality. Unlike the standard partial differential equation (PDE) modeling, the implicit calculus modeling approach does not require the explicit expression of the PDE governing equation. Instead the fundamental solution of physical problem is used to implicitly define the differential operator and to implement simulation in conjunction with the appropriate boundary conditions. In this study, we conjecture an extension of the fundamental solution of the standard Laplace and Helmholtz equations to negative dimensionality. And then by using the singular boundary method, a recent boundary discretization technique, we investigate the potential and wave problems using the fundamental solution on negative dimensionality. Numerical experiments reveal that the physics behaviors on negative dimensionality may differ on positive dimensionality. This speculative study might open an unexplored territory in research.

Characterization of Adhesives for Attaching Reusable Surface Insulation on Space Shuttle Vehicles

NASA Technical Reports Server (NTRS)

Owen, H. P.; Carroll, M. T.

1973-01-01

An extensive development and testing program on adhesive systems shows that: (1) A closed cell silicone rubber sponge bonded to substrates with thin bond lines of glass filled adhesive exhibits density and modulus values approximately one third that of solid silicone adhesives; (2) utilization of glass or phenolic microballoons as fillers in silicone adhesives reduces density but increases moduli of the vulcanized materials; (3) the silicone elastomer based adhesives appear to be complex systems rather than homogeneous, isotropic materials. Tensile, shear, and compression properties plotted versus temperature verify this conjecture; and (4) constant strain-stress relaxation tests on glass-filled adhesive show that stress relaxation is most pronounced near the glass transition temperature.

Neural mechanisms of motion sickness

NASA Technical Reports Server (NTRS)

Crampton, G. H.; Daunton, N. G.

1983-01-01

The possibility that there might be a neuro-homoral cerebrospinal fluid link in motion sickness was directly tested by blocking the flow of CSF from the third into the fourth ventricle in cats. Evidence obtained thus far is consistent with the hypothesis. Cats with demonstrably sound plugs did not vomit in response to an accelerative motion sickness stimulus, whereas cats with imperfect 'leaky' plugs vomited with little or no delay in latency. Althoough there are several putative candidates, the identification of a humoral motion sickness substance is a matter of conjecture.

Entropy Inequality Violations from Ultraspinning Black Holes.

PubMed

Hennigar, Robie A; Mann, Robert B; Kubizňák, David

2015-07-17

We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.

Maxwell's conjecture on three point charges with equal magnitudes

NASA Astrophysics Data System (ADS)

Tsai, Ya-Lun

2015-08-01

Maxwell's conjecture on three point charges states that the number of non-degenerate equilibrium points of the electrostatic field generated by them in R3 is at most four. We prove the conjecture in the cases when three point charges have equal magnitudes and show the number of isolated equilibrium points can only be zero, two, three, or four. Specifically, fixing positions of two positive charges in R3, we know exactly where to place the third positive charge to have two, three, or four equilibrium points. All equilibrium points are isolated and there are no other possibilities for the number of isolated equilibrium points. On the other hand, if both two of the fixed charges have negative charge values, there are always two equilibrium points except when the third positive charge lies in the line segment connecting the two negative charges. The exception cases are when the field contains only a curve of equilibrium points. In this paper, computations assisted by computer involve symbolic and exact integer computations. Therefore, all the results are proved rigorously.

Cosmic censorship conjecture in Kerr-Sen black hole

NASA Astrophysics Data System (ADS)

Gwak, Bogeun

2017-06-01

The validity of the cosmic censorship conjecture for the Kerr-Sen black hole, which is a solution to the low-energy effective field theory for four-dimensional heterotic string theory, is investigated using charged particle absorption. When the black hole absorbs the particle, the charge on it changes owing to the conserved quantities of the particle. Changes in the black hole are constrained to the equation for the motion of the particle and are consistent with the laws of thermodynamics. Particle absorption increases the mass of the Kerr-Sen black hole to more than that of the absorbed charges such as angular momentum and electric charge; hence, the black hole cannot be overcharged. In the near-extremal black hole, we observe a violation of the cosmic censorship conjecture for the angular momentum in the first order of expansion and the electric charge in the second order. However, considering an adiabatic process carrying the conserved quantities as those of the black hole, we prove the stability of the black hole horizon. Thus, we resolve the violation. This is consistent with the third law of thermodynamics.

Spacetime dynamics of a Higgs vacuum instability during inflation

DOE PAGES

East, William E.; Kearney, John; Shakya, Bibhushan; ...

2017-01-31

A remarkable prediction of the Standard Model is that, in the absence of corrections lifting the energy density, the Higgs potential becomes negative at large field values. If the Higgs field samples this part of the potential during inflation, the negative energy density may locally destabilize the spacetime. Here, we use numerical simulations of the Einstein equations to study the evolution of inflation-induced Higgs fluctuations as they grow towards the true (negative-energy) minimum. Our simulations show that forming a single patch of true vacuum in our past light cone during inflation is incompatible with the existence of our Universe; themore » boundary of the true vacuum region grows outward in a causally disconnected manner from the crunching interior, which forms a black hole. We also find that these black hole horizons may be arbitrarily elongated—even forming black strings—in violation of the hoop conjecture. Furthermore, by extending the numerical solution of the Fokker-Planck equation to the exponentially suppressed tails of the field distribution at large field values, we derive a rigorous correlation between a future measurement of the tensor-to-scalar ratio and the scale at which the Higgs potential must receive stabilizing corrections in order for the Universe to have survived inflation until today.« less

Karyotype Plasticity in Crickets: Numerical, Morphological, and Nucleolar Organizer Region Distribution Pattern of Anurogryllus sp.

PubMed Central

Cristina Schneider, Marielle; Ariza Zacaro, Adilson; Ferreira, Amilton; Maria Cella, Doralice

2010-01-01

Within the Orthopteran species, those of the suborder Ensifera have been rarely studied from the cytogenetic point of view, mainly due to the difficulties for taxonomic identification of its species. The Gryllidae is the second largest family of this suborder and possesses some genera, such as Anurogryllus, that occur only on the American continents. The aim of this work was to determine the karyotype characteristics, the meiotic chromosome behaviour, and the nucleolar organizer region (NOR) pattern of Anurogryllus sp (Orthoptera: Gryllidae). In the analyzed sample, high levels of numerical, morphological, and NORs polymorphisms were detected. Within five distinct karyotypes that were found, the basic karyotype of Anurogryllus sp. showed 2n(♂) = 22 + X0 with acrocentric autosomes and a metacentric X sex chromosome; furthermore, a conspicuous secondary constriction related to the NOR was present along the entire short arm on pair 5. The other four types of karyotypes arose from centric fusions between elements of pairs 1/3, 2/6, 4/7 and a NOR partial translocation from pair 5 onto the long arm terminal region of one element of the fused pair 2/6. Such intraspecific variability and the consequences of high levels of polymorphism are discussed, leading to conjectures about the mechanisms that led to these chromosome rearrangements. PMID:20673072

Driven fragmentation of granular gases.

PubMed

Cruz Hidalgo, Raúl; Pagonabarraga, Ignacio

2008-06-01

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the long velocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f(c) approximately exp(-cn) , with n approximately 1.2 , regarding less the fragmentation mechanisms.

Superuniversal transport near a (2 +1 ) -dimensional quantum critical point

NASA Astrophysics Data System (ADS)

Rose, F.; Dupuis, N.

2017-09-01

We compute the zero-temperature conductivity in the two-dimensional quantum O (N ) model using a nonperturbative functional renormalization-group approach. At the quantum critical point we find a universal conductivity σ*/σQ (with σQ=q2/h the quantum of conductance and q the charge) in reasonable quantitative agreement with quantum Monte Carlo simulations and conformal bootstrap results. In the ordered phase the conductivity tensor is defined, when N ≥3 , by two independent elements, σA(ω ) and σB(ω ) , respectively associated with SO (N ) rotations which do and do not change the direction of the order parameter. Whereas σA(ω →0 ) corresponds to the response of a superfluid (or perfect inductance), the numerical solution of the flow equations shows that limω→0σB(ω ) /σQ=σB*/σQ is a superuniversal (i.e., N -independent) constant. These numerical results, as well as the known exact value σB*/σQ=π /8 in the large-N limit, allow us to conjecture that σB*/σQ=π /8 holds for all values of N , a result that can be understood as a consequence of gauge invariance and asymptotic freedom of the Goldstone bosons in the low-energy limit.

Application of Hermitian time-dependent coupled-cluster response Ansätze of second order to excitation energies and frequency-dependent dipole polarizabilities

NASA Astrophysics Data System (ADS)

Wälz, Gero; Kats, Daniel; Usvyat, Denis; Korona, Tatiana; Schütz, Martin

2012-11-01

Linear-response methods, based on the time-dependent variational coupled-cluster or the unitary coupled-cluster model, and truncated at the second order according to the Møller-Plesset partitioning, i.e., the TD-VCC[2] and TD-UCC[2] linear-response methods, are presented and compared. For both of these methods a Hermitian eigenvalue problem has to be solved to obtain excitation energies and state eigenvectors. The excitation energies thus are guaranteed always to be real valued, and the eigenvectors are mutually orthogonal, in contrast to response theories based on “traditional” coupled-cluster models. It turned out that the TD-UCC[2] working equations for excitation energies and polarizabilities are equivalent to those of the second-order algebraic diagrammatic construction scheme ADC(2). Numerical tests are carried out by calculating TD-VCC[2] and TD-UCC[2] excitation energies and frequency-dependent dipole polarizabilities for several test systems and by comparing them to the corresponding values obtained from other second- and higher-order methods. It turns out that the TD-VCC[2] polarizabilities in the frequency regions away from the poles are of a similar accuracy as for other second-order methods, as expected from the perturbative analysis of the TD-VCC[2] polarizability expression. On the other hand, the TD-VCC[2] excitation energies are systematically too low relative to other second-order methods (including TD-UCC[2]). On the basis of these results and an analysis presented in this work, we conjecture that the perturbative expansion of the Jacobian converges more slowly for the TD-VCC formalism than for TD-UCC or for response theories based on traditional coupled-cluster models.

Inflation in a renormalizable cosmological model and the cosmic no hair conjecture

NASA Technical Reports Server (NTRS)

Maeda, Kei-Ichi; Stein-Schabes, Jaime A.; Futamase, Toshifumi

1988-01-01

The possibility of having inflation in a renormalizable cosmological model is investigated. The Cosmic No Hair Conjecture is proved to hold for all Bianchi types except Bianchi IX. By the use of a conformal transformation on the metric it is shown that these models are equivalent to the ones described by the Einstein-Hilbert action for gravity minimally coupled to a set of scalar fields with inflationary potentials. Henceforth, it is proven that inflationary solutions behave as attractors in solution space, making it a natural event in the evolution of such models.

On the structure of self-affine convex bodies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voynov, A S

2013-08-31

We study the structure of convex bodies in R{sup d} that can be represented as a union of their affine images with no common interior points. Such bodies are called self-affine. Vallet's conjecture on the structure of self-affine bodies was proved for d = 2 by Richter in 2011. In the present paper we disprove the conjecture for all d≥3 and derive a detailed description of self-affine bodies in R{sup 3}. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument. Bibliography: 10 titles.

A proof of the Biswas-Mitra-Bhattacharyya conjecture for the ideal quantum gas trapped under the generic power law potential U=\\sum\

NASA Astrophysics Data System (ADS)

Mehedi Faruk, Mir; Muktadir Rahman, Md

2016-03-01

The well known relation for ideal classical gas $\\Delta \\epsilon^2=kT^2 C_V$ which does not remain valid for quantum system is revisited. A new connection is established between energy fluctuation and specific heat for quantum gases, valid in the classical limit and the degenerate quantum regime as well. Most importantly the proposed Biswas-Mitra-Bhattacharyya (BMB) conjecture (Biswas $et.$ $al.$, J. Stat. Mech. P03013, 2015.) relating hump in energy fluctuation and discontinuity of specific heat is proved and precised in this manuscript.

A decomposition theory for phylogenetic networks and incompatible characters.

PubMed

Gusfield, Dan; Bansal, Vikas; Bafna, Vineet; Song, Yun S

2007-12-01

Phylogenetic networks are models of evolution that go beyond trees, incorporating non-tree-like biological events such as recombination (or more generally reticulation), which occur either in a single species (meiotic recombination) or between species (reticulation due to lateral gene transfer and hybrid speciation). The central algorithmic problems are to reconstruct a plausible history of mutations and non-tree-like events, or to determine the minimum number of such events needed to derive a given set of binary sequences, allowing one mutation per site. Meiotic recombination, reticulation and recurrent mutation can cause conflict or incompatibility between pairs of sites (or characters) of the input. Previously, we used "conflict graphs" and "incompatibility graphs" to compute lower bounds on the minimum number of recombination nodes needed, and to efficiently solve constrained cases of the minimization problem. Those results exposed the structural and algorithmic importance of the non-trivial connected components of those two graphs. In this paper, we more fully develop the structural importance of non-trivial connected components of the incompatibility and conflict graphs, proving a general decomposition theorem (Gusfield and Bansal, 2005) for phylogenetic networks. The decomposition theorem depends only on the incompatibilities in the input sequences, and hence applies to many types of phylogenetic networks, and to any biological phenomena that causes pairwise incompatibilities. More generally, the proof of the decomposition theorem exposes a maximal embedded tree structure that exists in the network when the sequences cannot be derived on a perfect phylogenetic tree. This extends the theory of perfect phylogeny in a natural and important way. The proof is constructive and leads to a polynomial-time algorithm to find the unique underlying maximal tree structure. We next examine and fully solve the major open question from Gusfield and Bansal (2005): Is it true that for every input there must be a fully decomposed phylogenetic network that minimizes the number of recombination nodes used, over all phylogenetic networks for the input. We previously conjectured that the answer is yes. In this paper, we show that the answer in is no, both for the case that only single-crossover recombination is allowed, and also for the case that unbounded multiple-crossover recombination is allowed. The latter case also resolves a conjecture recently stated in (Huson and Klopper, 2007) in the context of reticulation networks. Although the conjecture from Gusfield and Bansal (2005) is disproved in general, we show that the answer to the conjecture is yes in several natural special cases, and establish necessary combinatorial structure that counterexamples to the conjecture must possess. We also show that counterexamples to the conjecture are rare (for the case of single-crossover recombination) in simulated data.

Chen Jingrun, China's famous mathematician: devastated by brain injuries on the doorstep to solving a fundamental mathematical puzzle.

PubMed

Lei, Ting; Belykh, Evgenii; Dru, Alexander B; Yagmurlu, Kaan; Elhadi, Ali M; Nakaji, Peter; Preul, Mark C

2016-07-01

Chen Jingrun (1933-1996), perhaps the most prodigious mathematician of his time, focused on the field of analytical number theory. His work on Waring's problem, Legendre's conjecture, and Goldbach's conjecture led to progress in analytical number theory in the form of "Chen's Theorem," which he published in 1966 and 1973. His early life was ravaged by the Second Sino-Japanese War and the Chinese Cultural Revolution. On the verge of solving Goldbach's conjecture in 1984, Chen was struck by a bicyclist while also bicycling and suffered severe brain trauma. During his hospitalization, he was also found to have Parkinson's disease. Chen suffered another serious brain concussion after a fall only a few months after recovering from the bicycle crash. With significant deficits, he remained hospitalized for several years without making progress while receiving modern Western medical therapies. In 1988 traditional Chinese medicine experts were called in to assist with his treatment. After a year of acupuncture and oxygen therapy, Chen could control his basic bowel and bladder functions, he could walk slowly, and his swallowing and speech improved. When Chen was unable to produce complex work or finish his final work on Goldbach's conjecture, his mathematical pursuits were taken up vigorously by his dedicated students. He was able to publish Youth Math, a mathematics book that became an inspiration in Chinese education. Although he died in 1996 at the age of 63 after surviving brutal political repression, being deprived of neurological function at the very peak of his genius, and having to be supported by his wife, Chen ironically became a symbol of dedication, perseverance, and motivation to his students and associates, to Chinese youth, to a nation, and to mathematicians and scientists worldwide.

Large fluctuations of the macroscopic current in diffusive systems: a numerical test of the additivity principle.

PubMed

Hurtado, Pablo I; Garrido, Pedro L

2010-04-01

Most systems, when pushed out of equilibrium, respond by building up currents of locally conserved observables. Understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics. The additivity principle is a theoretical proposal that allows to compute the current distribution in many one-dimensional nonequilibrium systems. Using simulations, we validate this conjecture in a simple and general model of energy transport, both in the presence of a temperature gradient and in canonical equilibrium. In particular, we show that the current distribution displays a Gaussian regime for small current fluctuations, as prescribed by the central limit theorem, and non-Gaussian (exponential) tails for large current deviations, obeying in all cases the Gallavotti-Cohen fluctuation theorem. In order to facilitate a given current fluctuation, the system adopts a well-defined temperature profile different from that of the steady state and in accordance with the additivity hypothesis predictions. System statistics during a large current fluctuation is independent of the sign of the current, which implies that the optimal profile (as well as higher-order profiles and spatial correlations) are invariant upon current inversion. We also demonstrate that finite-time joint fluctuations of the current and the profile are well described by the additivity functional. These results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.

Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model.

PubMed

Bytchenkoff, Dimitri; Rodts, Stéphane

2011-01-01

The form of the two-dimensional (2D) NMR-relaxation spectra--which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T(1)) and spin-spin (T(2)) relaxation times--has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T(1)- and T(2)-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them--the presence of negative peaks--underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data. Copyright © 2010 Elsevier Inc. All rights reserved.

Critical phenomena at the threshold of immediate merger in binary black hole systems: The extreme mass ratio case

NASA Astrophysics Data System (ADS)

Gundlach, Carsten; Akcay, Sarp; Barack, Leor; Nagar, Alessandro

2012-10-01

In numerical simulations of black hole binaries, Pretorius and Khurana [Classical Quantum Gravity 24, S83 (2007)CQGRDG0264-938110.1088/0264-9381/24/12/S07] have observed critical behavior at the threshold between scattering and immediate merger. The number of orbits scales as n≃-γln⁡|p-p*| along any one-parameter family of initial data such that the threshold is at p=p*. Hence, they conjecture that in ultrarelativistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent γ. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by n∞≃0.41/η, where η is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter.

Group as social microcosm: Within-group interpersonal style is congruent with outside group relational tendencies.

PubMed

Goldberg, Simon B; Hoyt, William T

2015-06-01

The notion that individuals' interpersonal behaviors in the context of therapy reflects their interpersonal behaviors outside of therapy is a fundamental hypothesis underlying numerous systems of psychotherapy. The social microcosm hypothesis, in particular, claims the interpersonal therapy group becomes a reflection of group members' general tendencies, and can thus be used as information about members' interpersonal functioning as well as an opportunity for learning and behavior change. The current study tested this hypothesis using data drawn from 207 individuals participating in 22 interpersonal process groups. Ratings were made on 2 key interpersonal domains (Dominance and Affiliation) at baseline and at Weeks 2, 5, and 8 of the group. Two-level multilevel models (with participants nested within groups) were used to account for the hierarchical structure, and the social relations model (SRM; Kenny, 1994) was used to estimate peer ratings (target effects in SRM) unconfounded with rater bias. Participants showed consensus at all time points during the interpersonal process groups on one another's levels of dominance and affiliation. In addition, self- and peer ratings were stable across time and correlated with one another. Importantly, self-ratings made prior to group significantly predicted ratings (self- and peer) made within the group, with effect sizes within the medium range. Taken together, these results provide robust support for the social microcosm hypothesis and the conjecture that interpersonal style within-group therapy is reflective of broader interpersonal tendencies. (c) 2015 APA, all rights reserved).

Prolongation structures of nonlinear evolution equations. II

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1976-01-01

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer`s polynomial identities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warnaar, S.O.

1996-07-01

We compute the one-dimensional configuration sums of the AFB model using the fermionic techniques introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynominal identities for finitizations of the Virasoro characters {sub {chi}b, a}{sup (r-1, r)}(q) as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer`s identities and application of Bailey`s lemma.

On the mathematical foundations of mutually unbiased bases

NASA Astrophysics Data System (ADS)

Thas, Koen

2018-02-01

In order to describe a setting to handle Zauner's conjecture on mutually unbiased bases (MUBs) (stating that in C^d, a set of MUBs of the theoretical maximal size d + 1 exists only if d is a prime power), we pose some fundamental questions which naturally arise. Some of these questions have important consequences for the construction theory of (new) sets of maximal MUBs. Partial answers will be provided in particular cases; more specifically, we will analyze MUBs with associated operator groups that have nilpotence class 2, and consider MUBs of height 1. We will also confirm Zauner's conjecture for MUBs with associated finite nilpotent operator groups.

Two-point correlation function for Dirichlet L-functions

NASA Astrophysics Data System (ADS)

Bogomolny, E.; Keating, J. P.

2013-03-01

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

NASA Astrophysics Data System (ADS)

T. Sardari, Naser

2018-03-01

Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

Integrals of motion from quantum toroidal algebras

NASA Astrophysics Data System (ADS)

Feigin, B.; Jimbo, M.; Mukhin, E.

2017-11-01

We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors. That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model. We also discuss the ({gl_m, {gl_n) duality of XXZ models in quantum toroidal setting and the implications for the quantum KdV model. In particular, we conjecture that the spectrum of non-local integrals of motion of Bazhanov, Lukyanov, and Zamolodchikov is described by Gaudin Bethe ansatz equations associated to affine {sl}2 . Dedicated to the memory of Petr Petrovich Kulish.

Generalized clustering conditions of Jack polynomials at negative Jack parameter {alpha}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernevig, B. Andrei; Department of Physics, Princeton University, Princeton, New Jersey 08544; Haldane, F. D. M.

We present several conjectures on the behavior and clustering properties of Jack polynomials at a negative parameter {alpha}=-(k+1/r-1), with partitions that violate the (k,r,N)- admissibility rule of [Feigin et al. [Int. Math. Res. Notices 23, 1223 (2002)]. We find that the ''highest weight'' Jack polynomials of specific partitions represent the minimum degree polynomials in N variables that vanish when s distinct clusters of k+1 particles are formed, where s and k are positive integers. Explicit counting formulas are conjectured. The generalized clustering conditions are useful in a forthcoming description of fractional quantum Hall quasiparticles.

Clustering in the Three and Four Color Cyclic Particle Systems in One Dimension

NASA Astrophysics Data System (ADS)

Foxall, Eric; Lyu, Hanbaek

2018-03-01

We study the κ -color cyclic particle system on the one-dimensional integer lattice Z , first introduced by Bramson and Griffeath (Ann Prob:26-45, 1989). In that paper they show that almost surely, every site changes its color infinitely often if κ \\in {3,4} and only finitely many times if κ ≥ 5 . In addition, they conjecture that for κ \\in {3,4} the system clusters, that is, for any pair of sites x, y, with probability tending to 1 as t→ ∞, x and y have the same color at time t. Here we prove that conjecture.

On an inductive approach to the standard conjecture for a fibred complex variety with strong semistable degeneracies

NASA Astrophysics Data System (ADS)

Tankeev, S. G.

2017-12-01

We prove that Grothendieck's standard conjecture B(X) of Lefschetz type on the algebraicity of the operators \\ast and Λ of Hodge theory holds for a 4-dimensional smooth projective complex variety fibred over a smooth projective curve C provided that every degenerate fibre is a union of smooth irreducible components of multiplicity 1 with normal crossings, the standard conjecture B(X\\overlineη) holds for a generic geometric fibre X\\overlineη, there is at least one degenerate fibre X_δ and the rational cohomology rings H^\\ast(V_i,{Q}) and H^\\ast(V_i\\cap V_j,{Q}) of the irreducible components V_i of every degenerate fibre X_δ=V_1+ \\dots+ V_m are generated by classes of algebraic cycles. We obtain similar results for 3-dimensional fibred varieties with algebraic invariant cycles (defined by the smooth part π'\\colon X'\\to C' of the structure morphism π\\colon X\\to C) or with a degenerate fibre all of whose irreducible components E_i possess the property H^2(E_i,{Q})= \\operatorname{NS}(E_i)\\otimes{Z}{Q}.

A NUMERICAL SIMULATION OF COSMIC RAY MODULATION NEAR THE HELIOPAUSE. II. SOME PHYSICAL INSIGHTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Xi; Feng, Xueshang; Potgieter, Marius S.

Cosmic ray (CR) transport near the heliopause (HP) is studied using a hybrid transport model, with the parameters constrained by observations from the Voyager 1 spacecraft. We simulate the CR radial flux along different directions in the heliosphere. There is no well-defined thin layer between the solar wind region and the interstellar region along the tail and polar directions of the heliosphere. By analyzing the radial flux curve along the direction of Voyager 2 , together with its trajectory information, the crossing time of the HP by Voyager 2 is predicted to be in 2017.14. We simulate the CR radialmore » flux for different energy values along the direction of Voyager 1 . We find that there is only a modest modulation region of about 10 au wide beyond the HP, so that Voyager 1 observing the Local Interstellar Spectra is justified in numerical modeling. We analyze the heliospheric exit information of pseudo-particles in our stochastic numerical (time-backward) method, conjecturing that they represent the behavior of CR particles, and we find that pseudo-particles that have been traced from the nose region exit in the tail region. This implies that many CR particles diffuse directly from the heliospheric tail region to the nose region near the HP. In addition, when pseudo-particles were traced from the Local Interstellar Medium (LISM), it is found that their exit location (entrance for real particles) from the simulation domain is along the prescribed Interstellar Magnetic Field direction. This indicates that parallel diffusion dominates CR particle transport in the LISM.« less

Silicon photonic resonator sensors and devices

NASA Astrophysics Data System (ADS)

Chrostowski, Lukas; Grist, Samantha; Flueckiger, Jonas; Shi, Wei; Wang, Xu; Ouellet, Eric; Yun, Han; Webb, Mitch; Nie, Ben; Liang, Zhen; Cheung, Karen C.; Schmidt, Shon A.; Ratner, Daniel M.; Jaeger, Nicolas A. F.

2012-02-01

Silicon photonic resonators, implemented using silicon-on-insulator substrates, are promising for numerous applications. The most commonly studied resonators are ring/racetrack resonators. We have fabricated these and other resonators including disk resonators, waveguide-grating resonators, ring resonator reflectors, contra-directional grating-coupler ring resonators, and racetrack-based multiplexer/demultiplexers. While numerous resonators have been demonstrated for sensing purposes, it remains unclear as to which structures provide the highest sensitivity and best limit of detection; for example, disc resonators and slot-waveguide-based ring resonators have been conjectured to provide an improved limit of detection. Here, we compare various resonators in terms of sensor metrics for label-free bio-sensing in a micro-fluidic environment. We have integrated resonator arrays with PDMS micro-fluidics for real-time detection of biomolecules in experiments such as antigen-antibody binding reaction experiments using Human Factor IX proteins. Numerous resonators are fabricated on the same wafer and experimentally compared. We identify that, while evanescent-field sensors all operate on the principle that the analyte's refractive index shifts the resonant frequency, there are important differences between implementations that lie in the relationship between the optical field overlap with the analyte and the relative contributions of the various loss mechanisms. The chips were fabricated in the context of the CMC-UBC Silicon Nanophotonics Fabrication course and workshop. This yearlong, design-based, graduate training program is offered to students from across Canada and, over the last four years, has attracted participants from nearly every Canadian university involved in photonics research. The course takes students through a full design cycle of a photonic circuit, including theory, modelling, design, and experimentation.

Slippage on a particle-laden liquid-gas interface in textured microchannels

NASA Astrophysics Data System (ADS)

Gaddam, Anvesh; Agrawal, Amit; Joshi, Suhas S.; Thompson, Mark C.

2018-03-01

Despite numerous investigations in the literature on slip flows in textured microchannels, experimental results were seldom in agreement with the theory. It is conjectured that contamination of the liquid-gas interface by impurities might be one of the sources of this discrepancy. However, the effect of impurities on slippage at the liquid-gas interface is neither understood nor previously reported. To this end, this work presents numerical investigation on the flow past a liquid-gas interface embedded with solid particles in textured microchannels. Initially, we present numerical simulations past transverse ribs with cylindrical particles on the liquid-gas interface. A reduction in effective slip length (or slip loss) with respect to the particle-free interface as a function of gas fraction, constriction ratio, and particle position was quantified. A significant slip loss (˜20-80%) was induced, owing to acceleration-deceleration cycles experienced by the liquid advecting across the particle-laden liquid-gas interface. Even a small number of solid particles adsorbed on a liquid-gas interface were shown to reduce the effective slip length considerably. This renders a textured microchannel with the particle-laden interface to be ineffective as compared to a completely wetted textured microchannel under certain conditions. Furthermore, a flow past two bi-dimensional textures, viz. posts and holes, with their interfaces embedded with spherical particles was also simulated. Our results show that texture configurations with an unbounded liquid-gas interface can mitigate the detrimental effects of particles adsorbed at the interface. The results presented here will help guide in designing efficient textured surfaces in future.

Domain-area distribution anomaly in segregating multicomponent superfluids

NASA Astrophysics Data System (ADS)

Takeuchi, Hiromitsu

2018-01-01

The domain-area distribution in the phase transition dynamics of Z2 symmetry breaking is studied theoretically and numerically for segregating binary Bose-Einstein condensates in quasi-two-dimensional systems. Due to the dynamic-scaling law of the phase ordering kinetics, the domain-area distribution is described by a universal function of the domain area, rescaled by the mean distance between domain walls. The scaling theory for general coarsening dynamics in two dimensions hypothesizes that the distribution during the coarsening dynamics has a hierarchy with the two scaling regimes, the microscopic and macroscopic regimes with distinct power-law exponents. The power law in the macroscopic regime, where the domain size is larger than the mean distance, is universally represented with the Fisher's exponent of the percolation theory in two dimensions. On the other hand, the power-law exponent in the microscopic regime is sensitive to the microscopic dynamics of the system. This conjecture is confirmed by large-scale numerical simulations of the coupled Gross-Pitaevskii equation for binary condensates. In the numerical experiments of the superfluid system, the exponent in the microscopic regime anomalously reaches to its theoretical upper limit of the general scaling theory. The anomaly comes from the quantum-fluid effect in the presence of circular vortex sheets, described by the hydrodynamic approximation neglecting the fluid compressibility. It is also found that the distribution of superfluid circulation along vortex sheets obeys a dynamic-scaling law with different power-law exponents in the two regimes. An analogy to quantum turbulence on the hierarchy of vorticity distribution and the applicability to chiral superfluid 3He in a slab are also discussed.

Counting in Lattices: Combinatorial Problems from Statistical Mechanics.

NASA Astrophysics Data System (ADS)

Randall, Dana Jill

In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and self-avoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in higher dimensional lattices. We present the first efficient approximation algorithm for computing the number of matchings of any size in any periodic lattice in arbitrary dimension. The algorithm is based on Monte Carlo simulation of a suitable Markov chain and has rigorously derived performance guarantees that do not rely on any assumptions. In addition, we show that these results generalize to counting matchings in any graph which is the Cayley graph of a finite group. The second problem is counting self-avoiding walks in lattices. This problem arises in the study of the thermodynamics of long polymer chains in dilute solution. While there are a number of Monte Carlo algorithms used to count self -avoiding walks in practice, these are heuristic and their correctness relies on unproven conjectures. In contrast, we present an efficient algorithm which relies on a single, widely-believed conjecture that is simpler than preceding assumptions and, more importantly, is one which the algorithm itself can test. Thus our algorithm is reliable, in the sense that it either outputs answers that are guaranteed, with high probability, to be correct, or finds a counterexample to the conjecture. In either case we know we can trust our results and the algorithm is guaranteed to run in polynomial time. This is the first algorithm for counting self-avoiding walks in which the error bounds are rigorously controlled. This work was supported in part by an AT&T graduate fellowship, a University of California dissertation year fellowship and Esprit working group "RAND". Part of this work was done while visiting ICSI and the University of Edinburgh.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhdankin, Vladimir; Boldyrev, Stanislav; Perez, Jean Carlos

We investigate the intermittency of energy dissipation in magnetohydrodynamic (MHD) turbulence by identifying dissipative structures and measuring their characteristic scales. We find that the probability distribution of energy dissipation rates exhibits a power-law tail with an index very close to the critical value of –2.0, which indicates that structures of all intensities contribute equally to energy dissipation. We find that energy dissipation is uniformly spread among coherent structures with lengths and widths in the inertial range. At the same time, these structures have thicknesses deep within the dissipative regime. As the Reynolds number is increased, structures become thinner and moremore » numerous, while the energy dissipation continues to occur mainly in large-scale coherent structures. This implies that in the limit of high Reynolds number, energy dissipation occurs in thin, tightly packed current sheets which nevertheless span a continuum of scales up to the system size, exhibiting features of both coherent structures and nanoflares previously conjectured as a coronal heating mechanism.« less

Impact of heat source/sink on radiative heat transfer to Maxwell nanofluid subject to revised mass flux condition

NASA Astrophysics Data System (ADS)

Khan, M.; Irfan, M.; Khan, W. A.

2018-06-01

Nanofluids retain noteworthy structure that have absorbed attentions of numerous investigators because of their exploration in nanotechnology and nanoscience. In this scrutiny a mathematical computation of 2D flows of Maxwell nanoliquid influenced by a stretched cylinder has been established. The heat transfer structure is conceded out in the manifestation of thermal radiation and heat source/sink. Moreover, the nanoparticles mass flux condition is engaged in this exploration. This newly endorsed tactic is more realistic where the conjecture is made that the nanoparticle flux is zero and nanoparticle fraction regulates itself on the restrictions consequently. By utilizing apposite conversion the governing PDEs are transformed into ODEs and then tackled analytically via HAM. The attained outcomes are plotted and deliberated in aspect for somatic parameters. It is remarked that with an intensification in the Deborah number β diminish the liquid temperature while it boosts for radiation parameter Rd . Furthermore, the concentration of Maxwell liquid has conflicting impact for Brownian motion Nb and thermophoresis parameters Nt .

Scaling relations for watersheds

NASA Astrophysics Data System (ADS)

Fehr, E.; Kadau, D.; Araújo, N. A. M.; Andrade, J. S., Jr.; Herrmann, H. J.

2011-09-01

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical simulations. We find the fractal dimension of the watersheds to generally decrease with the Hurst exponent, which quantifies the degree of spatial correlations. Moreover, in two dimensions, our results match the range of fractal dimensions 1.10≤df≤1.15 observed for natural landscapes. We report that the watershed is strongly affected by local perturbations. For perturbed two and three dimensional systems, we observe a power-law scaling behavior for the distribution of areas (volumes) enclosed by the original and the displaced watershed and for the distribution of distances between outlets. Finite-size effects are analyzed and the resulting scaling exponents are shown to depend significantly on the Hurst exponent. The intrinsic relation between watershed and invasion percolation, as well as relations between exponents conjectured in previous studies with two dimensional systems, are now confirmed by our results in three dimensions.

Computation of Quasi-Periodic Normally Hyperbolic Invariant Tori: Algorithms, Numerical Explorations and Mechanisms of Breakdown

NASA Astrophysics Data System (ADS)

Canadell, Marta; Haro, Àlex

2017-12-01

We present several algorithms for computing normally hyperbolic invariant tori carrying quasi-periodic motion of a fixed frequency in families of dynamical systems. The algorithms are based on a KAM scheme presented in Canadell and Haro (J Nonlinear Sci, 2016. doi: 10.1007/s00332-017-9389-y), to find the parameterization of the torus with prescribed dynamics by detuning parameters of the model. The algorithms use different hyperbolicity and reducibility properties and, in particular, compute also the invariant bundles and Floquet transformations. We implement these methods in several 2-parameter families of dynamical systems, to compute quasi-periodic arcs, that is, the parameters for which 1D normally hyperbolic invariant tori with a given fixed frequency do exist. The implementation lets us to perform the continuations up to the tip of the quasi-periodic arcs, for which the invariant curves break down. Three different mechanisms of breakdown are analyzed, using several observables, leading to several conjectures.

Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation

NASA Technical Reports Server (NTRS)

Driscoll, Tobin A.; Vavasis, Stephen A.

1996-01-01

We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz-Christoffel transformation. The new algorithm, CRDT, is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT can never fail to converge to the correct Riemann mapping, but the correctness and convergence proof depend on conjectures that we have so far not been able to prove. We demonstrate convergence with computational experiments. The Riemann mapping has applications to problems in two-dimensional potential theory and to finite-difference mesh generation. We use CRDT to produce a mapping and solve a boundary value problem on long, thin regions for which no other algorithm can solve these problems.

Effective Hydraulic Conductivity of Three-Dimensional Heterogeneous Formations of Lognormal Permeability Distribution: The Impact of Connectivity

NASA Astrophysics Data System (ADS)

Zarlenga, A.; Janković, I.; Fiori, A.; Dagan, G.

2018-03-01

Uniform mean flow takes place in a 3-D heterogeneous formation of normal hydraulic logconductivity Y=ln⁡K. The aim of the study is to derive the dependence of the horizontal Kefh and vertical Kefv effective conductivities on the structural parameters of hydraulic conductivity and investigate the impact of departure from multi-Gaussianity on Kef, by numerical simulations of flow in formations that share the same pdf and covariance of Y but differ in the connectivity of classes of Y. The main result is that for the extreme models of connected and disconnected high Y zones the ratio between the effective conductivities in isotropic media is much smaller than in 2-D. The dependence of Kefh and Kefv upon the logconductivity variance and the anisotropy ratio is compared with existing approximations (first-order, Landau-Matheron conjecture, self-consistent approximation). Besides the theoretical interest, the results offer a basis for empirical relationships to be used in applications.

RIKEN BNL RESEARCH CENTER WORKSHOP ON GAUGE-INVARIANT VARIABLES IN GAUGE THEORIES, VOLUME 20

DOE Office of Scientific and Technical Information (OSTI.GOV)

VAN BAAL,P.; ORLAND,P.; PISARSKI,R.

2000-06-01

This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribovmore » copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.« less

Entanglement evolution across a conformal interface

NASA Astrophysics Data System (ADS)

Wen, Xueda; Wang, Yuxuan; Ryu, Shinsei

2018-05-01

For two-dimensional conformal field theories (CFTs) in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from to , where L is the length of the subsystem A, and is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e. a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with , where is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state.

Testing the null hypothesis: the forgotten legacy of Karl Popper?

PubMed

Wilkinson, Mick

2013-01-01

Testing of the null hypothesis is a fundamental aspect of the scientific method and has its basis in the falsification theory of Karl Popper. Null hypothesis testing makes use of deductive reasoning to ensure that the truth of conclusions is irrefutable. In contrast, attempting to demonstrate the new facts on the basis of testing the experimental or research hypothesis makes use of inductive reasoning and is prone to the problem of the Uniformity of Nature assumption described by David Hume in the eighteenth century. Despite this issue and the well documented solution provided by Popper's falsification theory, the majority of publications are still written such that they suggest the research hypothesis is being tested. This is contrary to accepted scientific convention and possibly highlights a poor understanding of the application of conventional significance-based data analysis approaches. Our work should remain driven by conjecture and attempted falsification such that it is always the null hypothesis that is tested. The write up of our studies should make it clear that we are indeed testing the null hypothesis and conforming to the established and accepted philosophical conventions of the scientific method.

Action and entanglement in gravity and field theory.

PubMed

Neiman, Yasha

2013-12-27

In nongravitational quantum field theory, the entanglement entropy across a surface depends on the short-distance regularization. Quantum gravity should not require such regularization, and it has been conjectured that the entanglement entropy there is always given by the black hole entropy formula evaluated on the entangling surface. We show that these statements have precise classical counterparts at the level of the action. Specifically, we point out that the action can have a nonadditive imaginary part. In gravity, the latter is fixed by the black hole entropy formula, while in nongravitating theories it is arbitrary. From these classical facts, the entanglement entropy conjecture follows by heuristically applying the relation between actions and wave functions.

Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated

NASA Astrophysics Data System (ADS)

Cator, E.; Van Mieghem, P.

2014-05-01

By invoking the famous Fortuin, Kasteleyn, and Ginibre (FKG) inequality, we prove the conjecture that the correlation of infection at the same time between any pair of nodes in a network cannot be negative for (exact) Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks. The truth of the conjecture establishes that the N-intertwined mean-field approximation (NIMFA) upper bounds the infection probability in any graph so that network design based on NIMFA always leads to safe protections against malware spread. However, when the infection or/and curing are not Poisson processes, the infection correlation between two nodes can be negative.

Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated.

PubMed

Cator, E; Van Mieghem, P

2014-05-01

By invoking the famous Fortuin, Kasteleyn, and Ginibre (FKG) inequality, we prove the conjecture that the correlation of infection at the same time between any pair of nodes in a network cannot be negative for (exact) Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks. The truth of the conjecture establishes that the N-intertwined mean-field approximation (NIMFA) upper bounds the infection probability in any graph so that network design based on NIMFA always leads to safe protections against malware spread. However, when the infection or/and curing are not Poisson processes, the infection correlation between two nodes can be negative.

Optimality of general lattice transformations with applications to the Bain strain in steel

NASA Astrophysics Data System (ADS)

Koumatos, K.; Muehlemann, A.

2016-04-01

This article provides a rigorous proof of a conjecture by E. C. Bain in 1924 on the optimality of the so-called Bain strain based on a criterion of least atomic movement. A general framework that explores several such optimality criteria is introduced and employed to show the existence of optimal transformations between any two Bravais lattices. A precise algorithm and a graphical user interface to determine this optimal transformation is provided. Apart from the Bain conjecture concerning the transformation from face-centred cubic to body-centred cubic, applications include the face-centred cubic to body-centred tetragonal transition as well as the transformation between two triclinic phases of terephthalic acid.

Perturbative Quantum Gravity from Gauge Theory

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph

In this dissertation we present the graphical techniques recently developed in the construction of multi-loop scattering amplitudes using the method of generalized unitarity. We construct the three-loop and four-loop four-point amplitudes of N = 8 supergravity using these methods and the Kawaii, Lewellen and Tye tree-level relations which map tree-level gauge theory amplitudes to tree-level gravity theory amplitudes. We conclude by extending a tree-level duality between color and kinematics, generic to gauge theories, to a loop level conjecture, allowing the easy relation between loop-level gauge and gravity kinematics. We provide non-trivial evidence for this conjecture at three-loops in the particular case of maximal supersymmetry.

FAST TRACK COMMUNICATION: Exact and simple results for the XYZ and strongly interacting fermion chains

NASA Astrophysics Data System (ADS)

Fendley, Paul; Hagendorf, Christian

2010-10-01

We conjecture exact and simple formulas for some physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey JxJy + JyJz + JxJz = 0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects.

Optimality of general lattice transformations with applications to the Bain strain in steel

PubMed Central

Koumatos, K.

2016-01-01

This article provides a rigorous proof of a conjecture by E. C. Bain in 1924 on the optimality of the so-called Bain strain based on a criterion of least atomic movement. A general framework that explores several such optimality criteria is introduced and employed to show the existence of optimal transformations between any two Bravais lattices. A precise algorithm and a graphical user interface to determine this optimal transformation is provided. Apart from the Bain conjecture concerning the transformation from face-centred cubic to body-centred cubic, applications include the face-centred cubic to body-centred tetragonal transition as well as the transformation between two triclinic phases of terephthalic acid. PMID:27274692

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

PubMed

Akemann, Gernot; Wettig, Tilo

2004-03-12

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.

Bare Quantum Null Energy Condition.

PubMed

Fu, Zicao; Marolf, Donald

2018-02-16

The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC is intrinsically finite. We study the more general case here where they do not and argue that a QNEC can still hold for bare (unrenormalized) quantities. While the original QNEC applied only to locally stationary null congruences in backgrounds that solve semiclassical theories of quantum gravity, at least in the formal perturbation theory at a small Planck length, the quantum focusing conjecture can be viewed as the special case of our bare QNEC for which the metric is on shell.

Learning to improve iterative repair scheduling

NASA Technical Reports Server (NTRS)

Zweben, Monte; Davis, Eugene

1992-01-01

This paper presents a general learning method for dynamically selecting between repair heuristics in an iterative repair scheduling system. The system employs a version of explanation-based learning called Plausible Explanation-Based Learning (PEBL) that uses multiple examples to confirm conjectured explanations. The basic approach is to conjecture contradictions between a heuristic and statistics that measure the quality of the heuristic. When these contradictions are confirmed, a different heuristic is selected. To motivate the utility of this approach we present an empirical evaluation of the performance of a scheduling system with respect to two different repair strategies. We show that the scheduler that learns to choose between the heuristics outperforms the same scheduler with any one of two heuristics alone.

On Born's Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal

NASA Astrophysics Data System (ADS)

Bétermin, Laurent; Knüpfer, Hans

2018-04-01

We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born's conjecture about the optimality of the rock salt alternate distribution of charges on a cubic lattice (and more generally on a d-dimensional orthorhombic lattice). Furthermore, we study this problem on the two-dimensional triangular lattice and we prove the optimality of a two-component honeycomb distribution of charges. The results hold for a class of completely monotone interaction potentials which includes Coulomb-type interactions for d≥3 . In a more general setting, we derive a connection between the optimal charge problem and a minimization problem for the translated lattice theta function.

Bare Quantum Null Energy Condition

NASA Astrophysics Data System (ADS)

Fu, Zicao; Marolf, Donald

2018-02-01

The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC is intrinsically finite. We study the more general case here where they do not and argue that a QNEC can still hold for bare (unrenormalized) quantities. While the original QNEC applied only to locally stationary null congruences in backgrounds that solve semiclassical theories of quantum gravity, at least in the formal perturbation theory at a small Planck length, the quantum focusing conjecture can be viewed as the special case of our bare QNEC for which the metric is on shell.

Time evolution of complexity in Abelian gauge theories

NASA Astrophysics Data System (ADS)

Hashimoto, Koji; Iizuka, Norihiro; Sugishita, Sotaro

2017-12-01

Quantum complexity is conjectured to probe inside of black hole horizons (or wormholes) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for Abelian pure gauge theories. For this purpose, we discretize the U (1 ) gauge group as ZN and also the continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories and to evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ˜exp (entropy), which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.

The minimal-ABC trees with B1-branches.

PubMed

Dimitrov, Darko; Du, Zhibin; Fonseca, Carlos M da

2018-01-01

The atom-bond connectivity index (or, for short, ABC index) is a molecular structure descriptor bridging chemistry to graph theory. It is probably the most studied topological index among all numerical parameters of a graph that characterize its topology. For a given graph G = (V, E), the ABC index of G is defined as [Formula: see text], where di denotes the degree of the vertex i, and ij is the edge incident to the vertices i and j. A combination of physicochemical and the ABC index properties are commonly used to foresee the bioactivity of different chemical composites. Additionally, the applicability of the ABC index in chemical thermodynamics and other areas of chemistry, such as in dendrimer nanostars, benzenoid systems, fluoranthene congeners, and phenylenes is well studied in the literature. While finding of the graphs with the greatest ABC-value is a straightforward assignment, the characterization of the tree(s) with minimal ABC index is a problem largely open and has recently given rise to numerous studies and conjectures. A B1-branch of a graph is a pendent path of order 2. In this paper, we provide an important step forward to the full characterization of these minimal trees. Namely, we show that a minimal-ABC tree contains neither 4 nor 3 B1-branches. The case when the number of B1-branches is 2 is also considered.

The Quantum Focussing Conjecture and Quantum Null Energy Condition

NASA Astrophysics Data System (ADS)

Koeller, Jason

Evidence has been gathering over the decades that spacetime and gravity are best understood as emergent phenomenon, especially in the context of a unified description of quantum mechanics and gravity. The Quantum Focussing Conjecture (QFC) and Quantum Null Energy Condition (QNEC) are two recently-proposed relationships between entropy and geometry, and energy and entropy, respectively, which further strengthen this idea. In this thesis, we study the QFC and the QNEC. We prove the QNEC in a variety of contexts, including free field theories on Killing horizons, holographic theories on Killing horizons, and in more general curved spacetimes. We also consider the implications of the QFC and QNEC in asymptotically flat space, where they constrain the information content of gravitational radiation arriving at null infinity, and in AdS/CFT, where they are related to other semiclassical inequalities and properties of boundary-anchored extremal area surfaces. It is shown that the assumption of validity and vacuum-state saturation of the QNEC for regions of flat space defined by smooth cuts of null planes implies a local formula for the modular Hamiltonian of these regions. We also demonstrate that the QFC as originally conjectured can be violated in generic theories in d ≥ 5, which led the way to an improved formulation subsequently suggested by Stefan Leichenauer.

Argyres-Douglas theories, the Macdonald index, and an RG inequality

DOE PAGES

Buican, Matthew; Nishinaka, Takahiro

2016-02-24

Here we conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A 1,A 2n₋3) and (A 1,D 2n) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two S-dualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a non-trivial set of renormalization group flows. Moreover, we demonstrate that, for certain values of n, our conjectures imply simple operator relations involving composites built out of the SU(2) R currents and flavor symmetry moment maps, and we findmore » a consistent picture in which these relations give rise to certain null states in the corresponding chiral algebras. In addition, we show that the Hall-Littlewood limits of our indices are equivalent to the corresponding Higgs branch Hilbert series. We explain this fact by considering the S 1 reductions of our theories and showing that the equivalence follows from an inequality on monopole quantum numbers whose coefficients are fixed by data of the four-dimensional parent theories. Finally, we comment on the implications of our work for more general $N = 2$ superconformal field theories.« less

Argyres-Douglas theories, the Macdonald index, and an RG inequality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buican, Matthew; Nishinaka, Takahiro

Here we conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A 1,A 2n₋3) and (A 1,D 2n) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two S-dualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a non-trivial set of renormalization group flows. Moreover, we demonstrate that, for certain values of n, our conjectures imply simple operator relations involving composites built out of the SU(2) R currents and flavor symmetry moment maps, and we findmore » a consistent picture in which these relations give rise to certain null states in the corresponding chiral algebras. In addition, we show that the Hall-Littlewood limits of our indices are equivalent to the corresponding Higgs branch Hilbert series. We explain this fact by considering the S 1 reductions of our theories and showing that the equivalence follows from an inequality on monopole quantum numbers whose coefficients are fixed by data of the four-dimensional parent theories. Finally, we comment on the implications of our work for more general $N = 2$ superconformal field theories.« less

A Schrödinger equation for solving the Bender-Brody-Müller conjecture

NASA Astrophysics Data System (ADS)

Moxley, Frederick Ira

2017-11-01

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and discuss the eigenvalues of the results. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, the Hilbert-Pólya conjecture is discussed, and it is heuristically shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

Detailed Analysis of the Interoccurrence Time Statistics in Seismic Activity

NASA Astrophysics Data System (ADS)

Tanaka, Hiroki; Aizawa, Yoji

2017-02-01

The interoccurrence time statistics of seismiciry is studied theoretically as well as numerically by taking into account the conditional probability and the correlations among many earthquakes in different magnitude levels. It is known so far that the interoccurrence time statistics is well approximated by the Weibull distribution, but the more detailed information about the interoccurrence times can be obtained from the analysis of the conditional probability. Firstly, we propose the Embedding Equation Theory (EET), where the conditional probability is described by two kinds of correlation coefficients; one is the magnitude correlation and the other is the inter-event time correlation. Furthermore, the scaling law of each correlation coefficient is clearly determined from the numerical data-analysis carrying out with the Preliminary Determination of Epicenter (PDE) Catalog and the Japan Meteorological Agency (JMA) Catalog. Secondly, the EET is examined to derive the magnitude dependence of the interoccurrence time statistics and the multi-fractal relation is successfully formulated. Theoretically we cannot prove the universality of the multi-fractal relation in seismic activity; nevertheless, the theoretical results well reproduce all numerical data in our analysis, where several common features or the invariant aspects are clearly observed. Especially in the case of stationary ensembles the multi-fractal relation seems to obey an invariant curve, furthermore in the case of non-stationary (moving time) ensembles for the aftershock regime the multi-fractal relation seems to satisfy a certain invariant curve at any moving times. It is emphasized that the multi-fractal relation plays an important role to unify the statistical laws of seismicity: actually the Gutenberg-Richter law and the Weibull distribution are unified in the multi-fractal relation, and some universality conjectures regarding the seismicity are briefly discussed.

Modeling Studies of PVT Growth of ZnSe: Current Status and Future Course

NASA Technical Reports Server (NTRS)

Ramachandran, N.; Su, Ching-Hua

1999-01-01

Bulk growth of wide band gap II-VI semiconductors by physical vapor transport (PVT) has been developed and refined over the past several years at NASA Marshall Space Flight Center. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using a two-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and a compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles are provided. The simulations show that the Stefan flux dominates the system flow field and the subtle gravitational effects can be gauged by subtracting this flux from the calculated profiles. Shear flows, due to solutal buoyancy, of the order of 50 microns/s for the liorizont,-d growth orientation and 10 microns/s for the vertical orientation are predicted. Whether these flows can fully account for the observed gravity related growth morphological effects and inhomogeneous solute and dopant distributions is a matter of conjecture. A template for future modeling efforts in this area is suggested which incorporates a mathematical approach to the tracking of the growth front based on energy of formation concepts.

Distance Constraint Satisfaction Problems

NASA Astrophysics Data System (ADS)

Bodirsky, Manuel; Dalmau, Victor; Martin, Barnaby; Pinsker, Michael

We study the complexity of constraint satisfaction problems for templates Γ that are first-order definable in ({ Z}; {suc}), the integers with the successor relation. Assuming a widely believed conjecture from finite domain constraint satisfaction (we require the tractability conjecture by Bulatov, Jeavons and Krokhin in the special case of transitive finite templates), we provide a full classification for the case that Γ is locally finite (i.e., the Gaifman graph of Γ has finite degree). We show that one of the following is true: The structure Γ is homomorphically equivalent to a structure with a certain majority polymorphism (which we call modular median) and CSP(Γ) can be solved in polynomial time, or Γ is homomorphically equivalent to a finite transitive structure, or CSP(Γ) is NP-complete.

Maximum time-dependent space-charge limited diode currents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Griswold, M. E.; Fisch, N. J.

Recent papers claim that a one dimensional (1D) diode with a time-varying voltage drop can transmit current densities that exceed the Child-Langmuir (CL) limit on average, apparently contradicting a previous conjecture that there is a hard limit on the average current density across any 1D diode, as t → ∞, that is equal to the CL limit. However, these claims rest on a different definition of the CL limit, namely, a comparison between the time-averaged diode current and the adiabatic average of the expression for the stationary CL limit. If the current were considered as a function of the maximummore » applied voltage, rather than the average applied voltage, then the original conjecture would not have been refuted.« less

Fate of the Hoop Conjecture in Quantum Gravity.

PubMed

Anzà, Fabio; Chirco, Goffredo

2017-12-08

We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Argyres, Philip C.; Lü, Yongchao; Martone, Mario

Coulomb branch chiral rings of N = 2 SCFTs are conjectured to be freely generated. While no counter-example is known, no direct evidence for the conjecture is known either. We initiate a systematic study of SCFTs with Coulomb branch chiral rings satisfying non-trivial relations, restricting our analysis to rank 1. The main result of our study is that (rank-1) SCFTs with non-freely generated CB chiral rings when deformed by relevant deformations, always flow to theories with non-freely generated CB rings. This implies that if they exist, they must thus form a distinct subset under RG flows. We also nd manymore » interesting characteristic properties that these putative theories satisfy which may be helpful in proving or disproving their existence using other methods.« less

Headphone and Head-Mounted Visual Displays for Virtual Environments

NASA Technical Reports Server (NTRS)

Begault, Duran R.; Ellis, Stephen R.; Wenzel, Elizabeth M.; Trejo, Leonard J. (Technical Monitor)

1998-01-01

A realistic auditory environment can contribute to both the overall subjective sense of presence in a virtual display, and to a quantitative metric predicting human performance. Here, the role of audio in a virtual display and the importance of auditory-visual interaction are examined. Conjectures are proposed regarding the effectiveness of audio compared to visual information for creating a sensation of immersion, the frame of reference within a virtual display, and the compensation of visual fidelity by supplying auditory information. Future areas of research are outlined for improving simulations of virtual visual and acoustic spaces. This paper will describe some of the intersensory phenomena that arise during operator interaction within combined visual and auditory virtual environments. Conjectures regarding audio-visual interaction will be proposed.

Tuition and Memory: mental models and cognitive processing in Japanese children's work on d.c. electrical circuits

NASA Astrophysics Data System (ADS)

Asami, Noriaki; King, Julien; Monk, Martin

2000-02-01

This paper looks at the familiar problem of students' understanding of elementary electrical circuits from a much neglected point of view. It is conjectured that the patterning commonly found in students' ideas might have its roots in the cognitive processing with which students operate their mental models of d.c. electrical circuits. The data are new and come from Japanese 10-11 year olds living in the UK. Progressive analysis of these students' answers to a six item test shows that the percentage of students operating particular mental models, following tuition, matches the percentages one might expect from a knowledge of their cognitive processing.

Collateral damage: the German food crisis, educational attainment and labor market outcomes of German post-war cohorts.

PubMed

Jürges, Hendrik

2013-01-01

Using the German 1970 census to study educational and labor market outcomes of cohorts born during the German food crisis after World War II, I document that those born between November 1945 and May 1946 have significantly lower educational attainment and occupational status than cohorts born shortly before or after. Several alternative explanations for this finding are tested. Most likely, a short spell of severe undernutrition around the end of the war has impaired intrauterine conditions in early pregnancies and resulted in long-term detriments among the affected cohorts. This conjecture is corroborated by evidence from Austria. Copyright © 2012 Elsevier B.V. All rights reserved.

Logic of discovery or psychology of invention?

NASA Astrophysics Data System (ADS)

Woodward, James F.

1992-02-01

It is noted that Popper separates the creation of concepts, conjectures, hypotheses and theories—the context of invention—from the testing thereof—the context of justification—arguing that only the latter is susceptible of rigorous logical analysis. Efforts on the part of others to shift or eradicate the demarcation established by this distinction are discussed and the relationship of these considerations to the claims of “strong artificial intelligence” is pointed out. It is argued that the mode of education of scientists, as well as reports of celebrated scientists, support Popper's judgement in this matter. An historical episode from Faraday's later career is used to illustrate the historiographical strength of Lakatos' “methodology of research programs.”

A combinatorial model for the Macdonald polynomials.

PubMed

Haglund, J

2004-11-16

We introduce a polynomial C(mu)[Z; q, t], depending on a set of variables Z = z(1), z(2),..., a partition mu, and two extra parameters q, t. The definition of C(mu) involves a pair of statistics (maj(sigma, mu), inv(sigma, mu)) on words sigma of positive integers, and the coefficients of the z(i) are manifestly in N[q,t]. We conjecture that C(mu)[Z; q, t] is none other than the modified Macdonald polynomial H(mu)[Z; q, t]. We further introduce a general family of polynomials F(T)[Z; q, S], where T is an arbitrary set of squares in the first quadrant of the xy plane, and S is an arbitrary subset of T. The coefficients of the F(T)[Z; q, S] are in N[q], and C(mu)[Z; q, t] is a sum of certain F(T)[Z; q, S] times nonnegative powers of t. We prove F(T)[Z; q, S] is symmetric in the z(i) and satisfies other properties consistent with the conjecture. We also show how the coefficient of a monomial in F(T)[Z; q, S] can be expressed recursively. maple calculations indicate the F(T)[Z; q, S] are Schur-positive, and we present a combinatorial conjecture for their Schur coefficients when the set T is a partition with at most three columns.

Optical Methods in Fingerprint Imaging for Medical and Personality Applications

PubMed Central

Wang, Jing-Wein; Lin, Ming-Hsun; Chang, Yao-Lang; Kuo, Chia-Ming

2017-01-01

Over the years, analysis and induction of personality traits has been a topic for individual subjective conjecture or speculation, rather than a focus of inductive scientific analysis. This study proposes a novel framework for analysis and induction of personality traits. First, 14 personality constructs based on the “Big Five” personality factors were developed. Next, a new fingerprint image algorithm was used for classification, and the fingerprints were classified into eight types. The relationship between personality traits and fingerprint type was derived from the results of the questionnaire survey. After comparison of pre-test and post-test results, this study determined the induction ability of personality traits from fingerprint type. Experimental results showed that the left/right thumbprint type of a majority of subjects was left loop/right loop and that the personalities of individuals with this fingerprint type were moderate with no significant differences in the 14 personality constructs. PMID:29065556

Precision lattice test of the gauge/gravity duality at large N

DOE PAGES

Berkowitz, Evan; Rinaldi, Enrico; Hanada, Masanori; ...

2016-11-03

We perform a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-N and continuum limits of the gauge theory are taken for the first time at various temperatures 0.4≤T≤1.0. As a way to test the gauge/gravity duality conjecture we compute the internal energy of the black hole as a function of the temperature directly from the gauge theory. We obtain a leading behavior that is compatible with the supergravity result E/N 2=7.41T 14/5: the coefficient is estimated to be 7.4±0.5 when the exponent is fixed and stringy corrections are included. This is the first confirmation of the supergravity predictionmore » for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. As a result, we also constrain stringy corrections to the internal energy.« less

Optical Methods in Fingerprint Imaging for Medical and Personality Applications.

PubMed

Wang, Chia-Nan; Wang, Jing-Wein; Lin, Ming-Hsun; Chang, Yao-Lang; Kuo, Chia-Ming

2017-10-23

Over the years, analysis and induction of personality traits has been a topic for individual subjective conjecture or speculation, rather than a focus of inductive scientific analysis. This study proposes a novel framework for analysis and induction of personality traits. First, 14 personality constructs based on the "Big Five" personality factors were developed. Next, a new fingerprint image algorithm was used for classification, and the fingerprints were classified into eight types. The relationship between personality traits and fingerprint type was derived from the results of the questionnaire survey. After comparison of pre-test and post-test results, this study determined the induction ability of personality traits from fingerprint type. Experimental results showed that the left/right thumbprint type of a majority of subjects was left loop/right loop and that the personalities of individuals with this fingerprint type were moderate with no significant differences in the 14 personality constructs.

Free-energy analysis of spin models on hyperbolic lattice geometries.

PubMed

Serina, Marcel; Genzor, Jozef; Lee, Yoju; Gendiar, Andrej

2016-04-01

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.

Breaking time reversal in a simple smooth chaotic system.

PubMed

Tomsovic, Steven; Ullmo, Denis; Nagano, Tatsuro

2003-06-01

Within random matrix theory, the statistics of the eigensolutions depend fundamentally on the presence (or absence) of time reversal symmetry. Accepting the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum systems with chaotic classical analogs. For practical reasons, much of the supporting numerical studies of symmetry breaking have been done with billiards or maps, and little with simple, smooth systems. There are two main difficulties in attempting to break time reversal invariance in a continuous time system with a smooth potential. The first is avoiding false time reversal breaking. The second is locating a parameter regime in which the symmetry breaking is strong enough to transform the fluctuation properties fully to the broken symmetry case, and yet remain weak enough so as not to regularize the dynamics sufficiently that the system is no longer chaotic. We give an example of a system of two coupled quartic oscillators whose energy level statistics closely match with those of the Gaussian unitary ensemble, and which possesses only a minor proportion of regular motion in its phase space.

Ineffective higher derivative black hole hair

NASA Astrophysics Data System (ADS)

Goldstein, Kevin; Mashiyane, James Junior

2018-01-01

Inspired by the possibility that the Schwarzschild black hole may not be the unique spherically symmetric vacuum solution to generalizations of general relativity, we consider black holes in pure fourth order higher derivative gravity treated as an effective theory. Such solutions may be of interest in addressing the issue of higher derivative hair or during the later stages of black hole evaporation. Non-Schwarzschild solutions have been studied but we have put earlier results on a firmer footing by finding a systematic asymptotic expansion for the black holes and matching them with known numerical solutions obtained by integrating out from the near-horizon region. These asymptotic expansions can be cast in the form of trans-series expansions which we conjecture will be a generic feature of non-Schwarzschild higher derivative black holes. Excitingly we find a new branch of solutions with lower free energy than the Schwarzschild solution, but as found in earlier work, solutions only seem to exist for black holes with large curvatures, meaning that one should not generically neglect even higher derivative corrections. This suggests that one effectively recovers the nonhair theorems in this context.

A Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation

NASA Astrophysics Data System (ADS)

Gwiazda, Piotr; Michálek, Martin; Świerczewska-Gwiazda, Agnieszka

2018-03-01

A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such cases most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable system of conservation laws; they are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake the role of physical admissibility conditions for weak solutions. We want to answer the question: what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality? An archetypal example of such a result was derived for the incompressible Euler system in the context of Onsager's conjecture in the early nineties. This general result can serve as a simple criterion to numerous systems of mathematical physics to prescribe the regularity of solutions needed for an appropriate companion law to be satisfied.

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

DOE Office of Scientific and Technical Information (OSTI.GOV)

McClean, Jarrod R.; Kimchi-Schwartz, Mollie E.; Carter, Jonathan

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channelmore » model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.« less

Triviality of Quantum Electrodynamics Revisited

NASA Astrophysics Data System (ADS)

Djukanovic, D.; Gegelia, J.; Meißner, Ulf-G.

2018-03-01

Quantum electrodynamics is often considered to be a trivial theory. This is based on a number of evidences, both numerical and analytical. One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling. We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections, the Landau pole is removed. We also analyze the cutoff dependence of the bare coupling at two-loop order and conclude that the conjecture, that for reasons of self-consistency, QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory. Supported in part by DFG and NSFC through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” National Natural Science Foundation of under Grant No. 11621131001, DFG under Grant No. TRR110, the Georgian Shota Rustaveli National Science Foundation (Grant FR/417/6-100/14) and the Chinese Academy of Sciences President’s International Fellowship Initiative (PIFI) under Grant No. 2017VMA0025

Three friendly walkers

NASA Astrophysics Data System (ADS)

Jensen, Iwan

2017-01-01

More than 15 years ago Guttmann and Vöge (2002 J. Stat. Plan. Inference 101 107), introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied model which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and in this case we prove that the friendly walkers generating function is the solution to a non-linear differential equation with polynomial coefficients, it is in other words D-algebraic. We find using numerically exact calculations a conjectured expression for the generating function of the original model as a ratio of a D-finite function and the generating function for vicious walkers. We obtain an expression for this D-finite function in terms of a {{}2}{{F}1} hypergeometric function with a rational pullback and its first and second derivatives. Dedicated to Tony Guttmann on the occasion of his 70th birthday.

High resolution gamma-ray spectroscopy and the fascinating angular momentum realm of the atomic nucleus

NASA Astrophysics Data System (ADS)

Riley, M. A.; Simpson, J.; Paul, E. S.

2016-12-01

In 1974 Aage Bohr and Ben Mottelson predicted the different ‘phases’ that may be expected in deformed nuclei as a function of increasing angular momentum and excitation energy all the way up to the fission limit. While admitting their picture was highly conjectural they confidently stated ‘...with the ingenious experimental approaches that are being developed, we may look forward with excitement to the detailed spectroscopic studies that will illuminate the behaviour of the spinning quantised nucleus’. High resolution gamma-ray spectroscopy has indeed been a major tool in studying the structure of atomic nuclei and has witnessed numerous significant advances over the last four decades. This article will select highlights from investigations at the Niels Bohr Institute, Denmark, and Daresbury Laboratory, UK, in the late 1970s and early 1980s, some of which have continued at other national laboratories in Europe and the USA to the present day. These studies illustrate the remarkable diversity of phenomena and symmetries exhibited by nuclei in the angular momentum-excitation energy plane that continue to surprise and fascinate scientists.

Constructing Current Singularity in a 3D Line-tied Plasma

DOE PAGES

Zhou, Yao; Huang, Yi-Min; Qin, Hong; ...

2017-12-27

We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finitemore » amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. Finally, with the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.« less

Surface segregation and the Al problem in GaAs quantum wells

NASA Astrophysics Data System (ADS)

Chung, Yoon Jang; Baldwin, K. W.; West, K. W.; Shayegan, M.; Pfeiffer, L. N.

2018-03-01

Low-defect two-dimensional electron systems (2DESs) are essential for studies of fragile many-body interactions that only emerge in nearly-ideal systems. As a result, numerous efforts have been made to improve the quality of modulation-doped AlxGa1 -xAs /GaAs quantum wells (QWs), with an emphasis on purifying the source material of the QW itself or achieving better vacuum in the deposition chamber. However, this approach overlooks another crucial component that comprises such QWs, the AlxGa1 -xAs barrier. Here we show that having a clean Al source and hence a clean barrier is instrumental to obtain a high-quality GaAs 2DES in a QW. We observe that the mobility of the 2DES in GaAs QWs declines as the thickness or Al content of the AlxGa1 -xAs barrier beneath the QW is increased, which we attribute to the surface segregation of oxygen atoms that originate from the Al source. This conjecture is supported by the improved mobility in the GaAs QWs as the Al cell is cleaned out by baking.

Linear monogamy of entanglement in three-qubit systems

NASA Astrophysics Data System (ADS)

Liu, Feng; Gao, Fei; Wen, Qiao-Yan

2015-11-01

For any three-qubit quantum systems ABC, Oliveira et al. numerically found that both the concurrence and the entanglement of formation (EoF) obey the linear monogamy relations in pure states. They also conjectured that the linear monogamy relations can be saturated when the focus qubit A is maximally entangled with the joint qubits BC. In this work, we prove analytically that both the concurrence and EoF obey linear monogamy relations in an arbitrary three-qubit state. Furthermore, we verify that all three-qubit pure states are maximally entangled in the bipartition A|BC when they saturate the linear monogamy relations. We also study the distribution of the concurrence and EoF. More specifically, when the amount of entanglement between A and B equals to that of A and C, we show that the sum of EoF itself saturates the linear monogamy relation, while the sum of the squared EoF is minimum. Different from EoF, the concurrence and the squared concurrence both saturate the linear monogamy relations when the entanglement between A and B equals to that of A and C.

Long-time behavior of material-surface curvature in isotropic turbulence

NASA Technical Reports Server (NTRS)

Girimaji, S. S.

1992-01-01

The behavior at large times of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. The main objectives are: to study the asymptotic behavior of the pdf curvature as a function of initial curvature and shape; and to establish whether the curvature of an initially plane material element goes to a stationary probability distribution. The evidence available in the literature about the asymptotic curvature-pdf of initially flat surfaces is ambiguous, and the conjecture is that it is quasi-stationary. In this work several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times the moments of the logarithm of curvature are independent of the initial pdf of curvature. This, it is argued, supports the view that the curvature attains a stationary distribution at long times. It is also shown that, irrespective of initial shape or curvature, the shape of any material element at long times is cylindrical with a high probability.

Dimension towers of SICs. I. Aligned SICs and embedded tight frames

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Bengtsson, Ingemar; Dumitru, Irina; Flammia, Steven

2017-11-01

Algebraic number theory relates SIC-POVMs in dimension d > 3 to those in dimension d(d - 2). We define a SIC in dimension d(d - 2) to be aligned to a SIC in dimension d if and only if the squares of the overlap phases in dimension d appear as a subset of the overlap phases in dimension d(d - 2) in a specified way. We give 19 (mostly numerical) examples of aligned SICs. We conjecture that given any SIC in dimension d, there exists an aligned SIC in dimension d(d - 2). In all our examples, the aligned SIC has lower dimensional equiangular tight frames embedded in it. If d is odd so that a natural tensor product structure exists, we prove that the individual vectors in the aligned SIC have a very special entanglement structure, and the existence of the embedded tight frames follows as a theorem. If d - 2 is an odd prime number, we prove that a complete set of mutually unbiased bases can be obtained by reducing an aligned SIC to this dimension.

Colloquium: Physics of the Riemann hypothesis

NASA Astrophysics Data System (ADS)

Schumayer, Dániel; Hutchinson, David A. W.

2011-04-01

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here a particular number-theoretical function is chosen, the Riemann zeta function, and its influence on the realm of physics is examined and also how physics may be suggestive for the resolution of one of mathematics’ most famous unconfirmed conjectures, the Riemann hypothesis. Does physics hold an essential key to the solution for this more than 100-year-old problem? In this work numerous models from different branches of physics are examined, from classical mechanics to statistical physics, where this function plays an integral role. This function is also shown to be related to quantum chaos and how its pole structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations light is shed on how the Riemann hypothesis can highlight physics. Naturally, the aim is not to be comprehensive, but rather focusing on the major models and aim to give an informed starting point for the interested reader.

Maximum of the modulus of kernels in Gauss-Turan quadratures

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.

2008-06-01

We study the kernels K_{n,s}(z) in the remainder terms R_{n,s}(f) of the Gauss-Turan quadrature formulae for analytic functions on elliptical contours with foci at pm 1 , when the weight omega is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel \\vert K_{n,s}(z)\\vert attains its maximum on the real axis (positive real semi-axis) for each ngeq n_0, n_0Dn_0(rho,s) . It was stated as a conjecture in [Mathematics of Computation 72 (2003), 1855-1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes n in the corresponding Gauss-Turan quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each ngeq n_0, n_0Dn_0(rho,s) . Numerical examples are included. Retrieve articles in all Journals with MSC (1991): [41]41A55, [42]65D30, [43]65D32

Shear viscosity of the quark-gluon plasma in a kinetic theory approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Puglisi, A.; Plumari, S.; Scardina, F.

2014-05-09

One of the main results of heavy ions collision (HIC) at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower bound η/s=1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green-Kubo relations give us an exact expression to compute these coefficients. We compute shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigate a system of particlesmore » interacting via anisotropic and energy dependent cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. The correct analytic formula for shear viscosity can be used to develop a transport theory with a fixed η/s and have a comparison with physical observables like elliptic flow.« less

Linear monogamy of entanglement in three-qubit systems.

PubMed

Liu, Feng; Gao, Fei; Wen, Qiao-Yan

2015-11-16

For any three-qubit quantum systems ABC, Oliveira et al. numerically found that both the concurrence and the entanglement of formation (EoF) obey the linear monogamy relations in pure states. They also conjectured that the linear monogamy relations can be saturated when the focus qubit A is maximally entangled with the joint qubits BC. In this work, we prove analytically that both the concurrence and EoF obey linear monogamy relations in an arbitrary three-qubit state. Furthermore, we verify that all three-qubit pure states are maximally entangled in the bipartition A|BC when they saturate the linear monogamy relations. We also study the distribution of the concurrence and EoF. More specifically, when the amount of entanglement between A and B equals to that of A and C, we show that the sum of EoF itself saturates the linear monogamy relation, while the sum of the squared EoF is minimum. Different from EoF, the concurrence and the squared concurrence both saturate the linear monogamy relations when the entanglement between A and B equals to that of A and C.

Linear monogamy of entanglement in three-qubit systems

PubMed Central

Liu, Feng; Gao, Fei; Wen, Qiao-Yan

2015-01-01

For any three-qubit quantum systems ABC, Oliveira et al. numerically found that both the concurrence and the entanglement of formation (EoF) obey the linear monogamy relations in pure states. They also conjectured that the linear monogamy relations can be saturated when the focus qubit A is maximally entangled with the joint qubits BC. In this work, we prove analytically that both the concurrence and EoF obey linear monogamy relations in an arbitrary three-qubit state. Furthermore, we verify that all three-qubit pure states are maximally entangled in the bipartition A|BC when they saturate the linear monogamy relations. We also study the distribution of the concurrence and EoF. More specifically, when the amount of entanglement between A and B equals to that of A and C, we show that the sum of EoF itself saturates the linear monogamy relation, while the sum of the squared EoF is minimum. Different from EoF, the concurrence and the squared concurrence both saturate the linear monogamy relations when the entanglement between A and B equals to that of A and C. PMID:26568265

Additivity Principle in High-Dimensional Deterministic Systems

NASA Astrophysics Data System (ADS)

Saito, Keiji; Dhar, Abhishek

2011-12-01

The additivity principle (AP), conjectured by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.180601], is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.

Ultra High Energy Cosmic Rays: Strangelets?

NASA Astrophysics Data System (ADS)

Xu, Ren-Xin; Wu, Fei

2003-06-01

The conjecture that ultra-high-energy cosmic rays (UHECRs) are actually strangelets is discussed. Besides the reason that strangelets can do as cosmic rays beyond the Greisen-Zatsepin-Kuzmin-cutoff, another argument to support the conjecture is addressed by the study of formation of TeV-scale microscopic black holes when UHECRs bombarding bare strange stars. It is proposed that the exotic quark surface of a bare strange star could be an effective astro-laboratory in the investigations of the extra dimensions and of the detection of ultra-high-energy neutrino fluxes. The flux of neutrinos (and other point-like particles) with energy larger than 2.3×1020 eV could be expected to be smaller than 10-26 cm-2 s-1 if there are two extra spatial dimensions.

Nutraceuticals and Their Potential to Treat Duchenne Muscular Dystrophy: Separating the Credible from the Conjecture

PubMed Central

Woodman, Keryn G.; Coles, Chantal A.; Lamandé, Shireen R.; White, Jason D.

2016-01-01

In recent years, complementary and alternative medicine has become increasingly popular. This trend has not escaped the Duchenne Muscular Dystrophy community with one study showing that 80% of caregivers have provided their Duchenne patients with complementary and alternative medicine in conjunction with their traditional treatments. These statistics are concerning given that many supplements are taken based on purely “anecdotal” evidence. Many nutraceuticals are thought to have anti-inflammatory or anti-oxidant effects. Given that dystrophic pathology is exacerbated by inflammation and oxidative stress these nutraceuticals could have some therapeutic benefit for Duchenne Muscular Dystrophy (DMD). This review gathers and evaluates the peer-reviewed scientific studies that have used nutraceuticals in clinical or pre-clinical trials for DMD and thus separates the credible from the conjecture. PMID:27834844

Nutraceuticals and Their Potential to Treat Duchenne Muscular Dystrophy: Separating the Credible from the Conjecture.

PubMed

Woodman, Keryn G; Coles, Chantal A; Lamandé, Shireen R; White, Jason D

2016-11-09

In recent years, complementary and alternative medicine has become increasingly popular. This trend has not escaped the Duchenne Muscular Dystrophy community with one study showing that 80% of caregivers have provided their Duchenne patients with complementary and alternative medicine in conjunction with their traditional treatments. These statistics are concerning given that many supplements are taken based on purely "anecdotal" evidence. Many nutraceuticals are thought to have anti-inflammatory or anti-oxidant effects. Given that dystrophic pathology is exacerbated by inflammation and oxidative stress these nutraceuticals could have some therapeutic benefit for Duchenne Muscular Dystrophy (DMD). This review gathers and evaluates the peer-reviewed scientific studies that have used nutraceuticals in clinical or pre-clinical trials for DMD and thus separates the credible from the conjecture.

A Reader's Guide to Gacs's "Positive Rates" Paper

NASA Astrophysics Data System (ADS)

Gray, Lawrence F.

2001-04-01

Peter Gacs's monograph, which follows this article, provides a counterexample to the important Positive Rates Conjecture. This conjecture, which arose in the late 1960's, was based on very plausible arguments, some of which come from statistical mechanics. During the long gestation period of the Gacs example, there has been a great deal of skepticism about the validity of his work. The construction and verification of Gacs's counterexample are unavoidably complex, and as a consequence, his paper is quite lengthy. But because of the novelty of the techniques and the significance of the result, his work deserves to become widely known. This reader's guide is intended both as a cheap substitute for reading the whole thing, as well as a warm-up for those who want to plumb its depths.

On the total bandwidth for the rational Harper's equation

NASA Astrophysics Data System (ADS)

Helffer, Bernard; Kerdelhué, Phillippe

1995-10-01

In the last years several contributions have been done around the total bandwidth of the spectrum for the Harper's operator. In particular an interesting conjecture has been proposed by Thouless which gives also strong convincing arguments for the proof in special cases. On the other hand, in the study of the Cantor structure of the spectrum, B. Helffer and J. Sjöstrand have justified an heuristic semiclassical approach proposed by M. Wilkinson. The aim of this article is to explain how one can use the first step of this approach to give a rigorous semi-classical proof of the Thouless formula in some of the simplest cases. We shall also indicate how one can hope with more effort to prove rigorously recent results of Last and Wilkinson on the same conjecture.

Energy conditions and junction conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marolf, Donald; Yaida, Sho; Mathematics Department, UCSB, Santa Barbara, California 93106

2005-08-15

We consider the familiar junction conditions described by Israel for thin timelike walls in Einstein-Hilbert gravity. One such condition requires the induced metric to be continuous across the wall. Now, there are many spacetimes with sources confined to a thin wall for which this condition is violated and the Israel formalism does not apply. However, we explore the conjecture that the induced metric is in fact continuous for any thin wall which models spacetimes containing only positive energy matter. Thus, the usual junction conditions would hold for all positive energy spacetimes. This conjecture is proven in various special cases, includingmore » the case of static spacetimes with spherical or planar symmetry as well as settings without symmetry which may be sufficiently well approximated by smooth spacetimes with well-behaved null geodesic congruences.« less

Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated

DOE PAGES

Argyres, Philip C.; Lü, Yongchao; Martone, Mario

2017-06-27

Coulomb branch chiral rings of N = 2 SCFTs are conjectured to be freely generated. While no counter-example is known, no direct evidence for the conjecture is known either. We initiate a systematic study of SCFTs with Coulomb branch chiral rings satisfying non-trivial relations, restricting our analysis to rank 1. The main result of our study is that (rank-1) SCFTs with non-freely generated CB chiral rings when deformed by relevant deformations, always flow to theories with non-freely generated CB rings. This implies that if they exist, they must thus form a distinct subset under RG flows. We also nd manymore » interesting characteristic properties that these putative theories satisfy which may be helpful in proving or disproving their existence using other methods.« less

Scanning the parameter space of collapsing rotating thin shells

NASA Astrophysics Data System (ADS)

Rocha, Jorge V.; Santarelli, Raphael

2018-06-01

We present results of a comprehensive study of collapsing and bouncing thin shells with rotation, framing it in the context of the weak cosmic censorship conjecture. The analysis is based on a formalism developed specifically for higher odd dimensions that is able to describe the dynamics of collapsing rotating shells exactly. We analyse and classify a plethora of shell trajectories in asymptotically flat spacetimes. The parameters varied include the shell’s mass and angular momentum, its radial velocity at infinity, the (linear) equation-of-state parameter and the spacetime dimensionality. We find that plunges of rotating shells into black holes never produce naked singularities, as long as the matter shell obeys the weak energy condition, and so respects cosmic censorship. This applies to collapses of dust shells starting from rest or with a finite velocity at infinity. Not even shells with a negative isotropic pressure component (i.e. tension) lead to the formation of naked singularities, as long as the weak energy condition is satisfied. Endowing the shells with a positive isotropic pressure component allows for the existence of bouncing trajectories satisfying the dominant energy condition and fully contained outside rotating black holes. Otherwise any turning point occurs always inside the horizon. These results are based on strong numerical evidence from scans of numerous sections in the large parameter space available to these collapsing shells. The generalisation of the radial equation of motion to a polytropic equation-of-state for the matter shell is also included in an appendix.

Self-duality and phase structure of the 4D random-plaquette Z2 gauge model

NASA Astrophysics Data System (ADS)

Arakawa, Gaku; Ichinose, Ikuo; Matsui, Tetsuo; Takeda, Koujin

2005-03-01

In the present paper, we shall study the 4-dimensional Z lattice gauge model with a random gauge coupling; the random-plaquette gauge model (RPGM). The random gauge coupling at each plaquette takes the value J with the probability 1-p and - J with p. This model exhibits a confinement-Higgs phase transition. We numerically obtain a phase boundary curve in the (p-T)-plane where T is the "temperature" measured in unit of J/k. This model plays an important role in estimating the accuracy threshold of a quantum memory of a toric code. In this paper, we are mainly interested in its "self-duality" aspect, and the relationship with the random-bond Ising model (RBIM) in 2-dimensions. The "self-duality" argument can be applied both for RPGM and RBIM, giving the same duality equations, hence predicting the same phase boundary. The phase boundary curve obtained by our numerical simulation almost coincides with this predicted phase boundary at the high-temperature region. The phase transition is of first order for relatively small values of p<0.08, but becomes of second order for larger p. The value of p at the intersection of the phase boundary curve and the Nishimori line is regarded as the accuracy threshold of errors in a toric quantum memory. It is estimated as p=0.110±0.002, which is very close to the value conjectured by Takeda and Nishimori through the "self-duality" argument.

Potts-model formulation of the random resistor network

NASA Astrophysics Data System (ADS)

Harris, A. B.; Lubensky, T. C.

1987-05-01

The randomly diluted resistor network is formulated in terms of an n-replicated s-state Potts model with a spin-spin coupling constant J in the limit when first n, then s, and finally 1/J go to zero. This limit is discussed and to leading order in 1/J the generalized susceptibility is shown to reproduce the results of the accompanying paper where the resistor network is treated using the xy model. This Potts Hamiltonian is converted into a field theory by the usual Hubbard-Stratonovich transformation and thereby a renormalization-group treatment is developed to obtain the corrections to the critical exponents to first order in ɛ=6-d, where d is the spatial dimensionality. The recursion relations are shown to be the same as for the xy model. Their detailed analysis (given in the accompanying paper) gives the resistance crossover exponent as φ1=1+ɛ/42, and determines the critical exponent, t for the conductivity of the randomly diluted resistor network at concentrations, p, just above the percolation threshold: t=(d-2)ν+φ1, where ν is the critical exponent for the correlation length at the percolation threshold. These results correct previously accepted results giving φ=1 to all orders in ɛ. The new result for φ1 removes the paradox associated with the numerical result that t>1 for d=2, and also shows that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, since it disagrees with the ɛ expansion.

Geomagnetic Secular Variation Prediction with Thermal Heterogeneous Boundary Conditions

NASA Astrophysics Data System (ADS)

Kuang, W.; Tangborn, A.; Jiang, W.

2011-12-01

It has long been conjectured that thermal heterogeneity at the core-mantle boundary (CMB) affects the geodynamo substantially. The observed two pairs of steady and strong magnetic flux lobes near the Polar Regions and the low secular variation in the Pacific over the past 400 years (and perhaps longer) are likely the consequences of this CMB thermal heterogeneity. There are several studies on the impact of the thermal heterogeneity with numerical geodynamo simulations. However, direct correlation between the numerical results and the observations is found very difficult, except qualitative comparisons of certain features in the radial component of the magnetic field at the CMB. This makes it difficult to assess accurately the impact of thermal heterogeneity on the geodynamo and the geomagnetic secular variation. We revisit this problem with our MoSST_DAS system in which geomagnetic data are assimilated with our geodynamo model to predict geomagnetic secular variations. In this study, we implement a heterogeneous heat flux across the CMB that is chosen based on the seismic tomography of the lowermost mantle. The amplitude of the heat flux (relative to the mean heat flux across the CMB) varies in the simulation. With these assimilation studies, we will examine the influences of the heterogeneity on the forecast accuracies, e.g. the accuracies as functions of the heterogeneity amplitude. With these, we could be able to assess the model errors to the true core state, and thus the thermal heterogeneity in geodynamo modeling.

Projectile Motion with Mathematica.

ERIC Educational Resources Information Center

de Alwis, Tilak

2000-01-01

Describes how to use the computer algebra system (CAS) Mathematica to analyze projectile motion with and without air resistance. These experiments result in several conjectures leading to theorems. (Contains 17 references.) (Author/ASK)

The risks associated with falling parts of glazed facades in case of fire

NASA Astrophysics Data System (ADS)

Sędłak, Bartłomiej; Kinowski, Jacek; Sulik, Paweł; Kimbar, Grzegorz

2018-05-01

Arguably, one of the most important requirement a building have to meet in case of fire is to ensure the safe evacuation of its users and the work of rescue teams. Consequently, issues related to the risks associated with falling parts of facades are fairly well known around Europe. Even though not equally well defined as other fire safety requirements concerning glazed facades, there is plenty of test methods for assessment of facades regarding falling parts, mostly based on an approach related to fire spread. In this paper selection of test method for assessment of facades regarding falling parts is briefly presented. However, focus of this work is on fire test of typical glazed segment of façade performed in ITB Laboratory. Results of the test positively verifies conjecture that solutions with glass units configured with thin, tempered glass panes on the outer side should pose no threat. However, the question has been raised whether the behaviour of other glass unit solutions (with additional coatings or laminated) would be similar.

Activities for Calculators.

ERIC Educational Resources Information Center

Hiatt, Arthur A.

1987-01-01

Ten activities that give learners in grades 5-8 a chance to explore mathematics with calculators are provided. The activity cards involve such topics as odd addends, magic squares, strange projects, and conjecturing rules. (MNS)

The Truth with Some Stretchers.

ERIC Educational Resources Information Center

Girard, Linda W.

1988-01-01

Discusses the biographies of Jean Fritz, demonstrating that in the hands of an artist, biography benefits from the use of the conjectural tools of fiction, such as created dialogue or interior monologue. (ARH)

Layer-dependent role of collagen recruitment during loading of the rat bladder wall.

PubMed

Cheng, Fangzhou; Birder, Lori A; Kullmann, F Aura; Hornsby, Jack; Watton, Paul N; Watkins, Simon; Thompson, Mark; Robertson, Anne M

2018-04-01

In this work, we re-evaluated long-standing conjectures as to the source of the exceptionally large compliance of the bladder wall. Whereas these conjectures were based on indirect measures of loading mechanisms, in this work we take advantage of advances in bioimaging to directly assess collagen fibers and wall architecture during biaxial loading. A custom biaxial mechanical testing system compatible with multiphoton microscopy was used to directly measure the layer-dependent collagen fiber recruitment in bladder tissue from 9 male Fischer rats (4 adult and 5 aged). As for other soft tissues, the bladder loading curve was exponential in shape and could be divided into toe, transition and high stress regimes. The relationship between collagen recruitment and loading curves was evaluated in the context of the inner (lamina propria) and outer (detrusor smooth muscle) layers. The large extensibility of the bladder was found to be possible due to folds in the wall (rugae) that provide a mechanism for low resistance flattening without any discernible recruitment of collagen fibers throughout the toe regime. For more extensible bladders, as the loading extended into the transition regime, a gradual coordinated recruitment of collagen fibers between the lamina propria layer and detrusor smooth muscle layer was found. A second important finding was that wall extensibility could be lost by premature recruitment of collagen in the outer wall that cut short the toe region. This change was correlated with age. This work provides, for the first time, a mechanistic understanding of the role of collagen recruitment in determining bladder extensibility and capacitance.

20. Photocopy of drawing (Original in collection of Price & ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

20. Photocopy of drawing (Original in collection of Price & Dickey, Architects) CONJECTURAL RESTORATION OF EAST ROOM, FIRST FLOOR - Caleb Pusey House, 15 Race Street (Landingford Plantation), Upland, Delaware County, PA

Does parental consent for birth control affect underage pregnancy rates? The case of Texas.

PubMed

Girma, Sourafel; Paton, David

2013-12-01

Previous work based on conjectural responses of minors predicted that the 2003 Texas requirement for parental consent for state-funded birth control to minors would lead to a large increase in underage pregnancies. We use state- and county-level data to test this prediction. The latter allow us to compare the impact of parental consent in counties with and without state-funded family planning clinics. We control for characteristics systematically correlated with the presence of state-funded clinics by combining difference-in-difference estimation with propensity score-weighted regressions. The evidence suggests that the parental consent mandate led to a large decrease in attendance at family planning clinics among teens but did not lead to an increase in underage pregnancies.

Do event horizons exist?

NASA Astrophysics Data System (ADS)

Baccetti, Valentina; Mann, Robert B.; Terno, Daniel R.

Event horizons are the defining feature of classical black holes. They are the key ingredient of the information loss paradox which, as paradoxes in quantum foundations, is built on a combination of predictions of quantum theory and counterfactual classical features: neither horizon formation nor its crossing by a test body can be detected by a distant observer. Furthermore, horizons are unnecessary for the production of Hawking-like radiation. We demonstrate that when this radiation is taken into account, it can prevent horizon crossing/formation in a large class of models. We conjecture that horizon avoidance is a general feature of collapse. The nonexistence of event horizons dispels the paradox, but opens up important questions about thermodynamic properties of the resulting objects and correlations between different degrees of freedom.

Approximation by the iterates of Bernstein operator

NASA Astrophysics Data System (ADS)

Zapryanova, Teodora; Tachev, Gancho

2012-11-01

We study the degree of pointwise approximation of the iterated Bernstein operators to its limiting operator. We obtain a quantitative estimates related to the conjecture of Gonska and Raşa from 2006.

Théorie de Lubin-Tate non-abélienne et représentations elliptiques

NASA Astrophysics Data System (ADS)

Dat, J.-F.

2007-03-01

Harris and Taylor proved that the supercuspidal part of the cohomology of the Lubin-Tate tower realizes both the local Langlands and Jacquet-Langlands correspondences, as conjectured by Carayol. Recently, Boyer computed the remaining part of the cohomology and exhibited two defects : first, the representations of GL\\_d which appear are of a very particular and restrictive form ; second, the Langlands correspondence is not realized anymore. In this paper, we study the cohomology complex in a suitable equivariant derived category, and show how it encodes Langlands correspondance for all elliptic representations. Then we transfer this result to the Drinfeld tower via an enhancement of a theorem of Faltings due to Fargues. We deduce that Deligne's weight-monodromy conjecture is true for varieties uniformized by Drinfeld's coverings of his symmetric spaces.

Optimal population size and endogenous growth.

PubMed

Palivos, T; Yip, C K

1993-01-01

"Many applications in economics require the selection of an objective function which enables the comparison of allocations involving different population sizes. The two most commonly used criteria are the Benthamite and the Millian welfare functions, also known as classical and average utilitarianism, respectively. The former maximizes total utility of the society and thus represents individuals, while the latter maximizes average utility and so represents generations. Edgeworth (1925) was the first to conjecture, that the Benthamite principle leads to a larger population size and a lower standard of living.... The purpose of this paper is to examine Edgeworth's conjecture in an endogenous growth framework in which there are interactions between output and population growth rates. It is shown that, under conditions that ensure an optimum, the Benthamite criterion leads to smaller population and higher output growth rates than the Millian." excerpt

Elucidation of covariant proofs in general relativity: example of the use of algebraic software in the shear-free conjecture in MAPLE

NASA Astrophysics Data System (ADS)

Huf, P. A.; Carminati, J.

2018-01-01

In this paper we explore the use of a new algebraic software package in providing independent covariant proof of a conjecture in general relativity. We examine the proof of two sub-cases of the shear-free conjecture σ =0 => ω Θ =0 by Senovilla et al. (Gen. Relativ. Gravit 30:389-411, 1998): case 1: for dust; case 2: for acceleration parallel to vorticity. We use TensorPack, a software package recently released for the Maple environment. In this paper, we briefly summarise the key features of the software and then demonstrate its use by providing and discussing examples of independent proofs of the paper in question. A full set of our completed proofs is available online at http://www.bach2roq.com/science/maths/GR/ShearFreeProofs.html. We are in agreeance with the equations provided in the original paper, noting that the proofs often require many steps. Furthermore, in our proofs we provide fully worked algebraic steps in such a way that the proofs can be examined systematically, and avoiding hand calculation. It is hoped that the elucidated proofs may be of use to other researchers in verifying the algebraic consistency of the expressions in the paper in question, as well as related literature. Furthermore we suggest that the appropriate use of algebraic software in covariant formalism could be useful for developing research and teaching in GR theory.

Dreams of Tigers and Flowers: Child Gender Predictions and Preference in an Urban Mainland Chinese Sample during Pregnancy

PubMed Central

Loo, Kek Khee; Luo, Xiying; Su, Hong; Presson, Angela; Li, Yan

2009-01-01

In an urban, mainland Chinese sample, we investigated expectant mothers’ stated gender preference for a boy or girl child, their conjectures on the fetal gender, the culture-specific beliefs for making their predictions, and their relations to sociodemographic variables. A total of 174 women were interviewed at 12–19 weeks gestation. Among 84 women who made a prediction on gender, 56 (67%) thought they were carrying a boy, and 28 (33%) expected a girl. The most frequent reasons cited for their speculation were personal feelings (36%), food/taste preference (13%), feedback from others (13%), somatic responses (13%) and dreams (7%). Out of 63 women who stated a wish for a boy or girl child, 45 (71%) wished for a girl and 18 (29%) wished for a boy. Women with undergraduate or graduate degrees were more likely to indicate a preference for boys. Older expectant mothers were more likely to report that they thought they were carrying boys. In conclusion, the majority of the women did not state a distinct choice for gender of the child. When they expressed a gender preference, more mothers expressed a desire to have a girl. However, boy child conjectures were more frequent than girl child conjectures. Greater boy child preference and prediction among the most highly educated and older expectant mothers might be reflective of implicit social status in having sons in urban China. PMID:19485234

Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

NASA Technical Reports Server (NTRS)

Frank, Adam; Jones, T. W.; Ryu, Dongsu

1995-01-01

Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.

Finite Inflation, Holography, and Dark Matter Annihilation

NASA Astrophysics Data System (ADS)

Scacco, Andrew Joseph

This thesis covers work on theoretical cosmology relating to inflation, de Sitter space, dark matter annihilation, and holography. A unifying feature of all these topics is that all of them occur in de Sitter space or focus on epochs of the Universe when the spacetime was close to de Sitter and that all of them have some connection to holography. Chapter 1 provides a pedagogical introduction to the fundamentals of cosmology, inflation, de Sitter space, dark matter annihilation and entanglement entropy. Chapter 2 covers the impact on the causal entropic principle of dark matter annihilation that we find to have the greatest relevance at late times in the future when the dark energy has driven the universe to be asymptotically de Sitter. In this chapter we estimate holographically preferred dark matter properties for a range of assumptions. Chapter 3 covers holographic bounds in models of finite inflation, specifically the Banks-Fischler bound and de Sitter equilibrium. The assumptions in each of these models are explored in detail and some interesting new connections are presented. Chapter 4 tests models of inflation with a fast-roll start that happen to satisfy the holographic bounds in Chapter 3 against cosmic microwave background data from Planck. We find a slight preference for a feature at the scale predicted by the Banks-Fischler bound though this preference is not found to be statistically significant. Chapter 5 contains a numerical computation of the holographic mutual information for an annular configuration of regions on a conformal field theory in de Sitter space using the AdS/CFT correspondence. This computation shows that the de Sitter space CFT entanglement entropy matches what would be expected from a Minkowski CFT and shows that the HRT conjecture works for this case.

A genome-wide association study of autism using the Simons Simplex Collection: Does reducing phenotypic heterogeneity in autism increase genetic homogeneity?

PubMed

Chaste, Pauline; Klei, Lambertus; Sanders, Stephan J; Hus, Vanessa; Murtha, Michael T; Lowe, Jennifer K; Willsey, A Jeremy; Moreno-De-Luca, Daniel; Yu, Timothy W; Fombonne, Eric; Geschwind, Daniel; Grice, Dorothy E; Ledbetter, David H; Mane, Shrikant M; Martin, Donna M; Morrow, Eric M; Walsh, Christopher A; Sutcliffe, James S; Lese Martin, Christa; Beaudet, Arthur L; Lord, Catherine; State, Matthew W; Cook, Edwin H; Devlin, Bernie

2015-05-01

Phenotypic heterogeneity in autism has long been conjectured to be a major hindrance to the discovery of genetic risk factors, leading to numerous attempts to stratify children based on phenotype to increase power of discovery studies. This approach, however, is based on the hypothesis that phenotypic heterogeneity closely maps to genetic variation, which has not been tested. Our study examines the impact of subphenotyping of a well-characterized autism spectrum disorder (ASD) sample on genetic homogeneity and the ability to discover common genetic variants conferring liability to ASD. Genome-wide genotypic data of 2576 families from the Simons Simplex Collection were analyzed in the overall sample and phenotypic subgroups defined on the basis of diagnosis, IQ, and symptom profiles. We conducted a family-based association study, as well as estimating heritability and evaluating allele scores for each phenotypic subgroup. Association analyses revealed no genome-wide significant association signal. Subphenotyping did not increase power substantially. Moreover, allele scores built from the most associated single nucleotide polymorphisms, based on the odds ratio in the full sample, predicted case status in subsets of the sample equally well and heritability estimates were very similar for all subgroups. In genome-wide association analysis of the Simons Simplex Collection sample, reducing phenotypic heterogeneity had at most a modest impact on genetic homogeneity. Our results are based on a relatively small sample, one with greater homogeneity than the entire population; if they apply more broadly, they imply that analysis of subphenotypes is not a productive path forward for discovering genetic risk variants in ASD. Copyright © 2015 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

A theory of stationarity and asymptotic approach in dissipative systems

NASA Astrophysics Data System (ADS)

Rubel, Michael Thomas

2007-05-01

The approximate dynamics of many physical phenomena, including turbulence, can be represented by dissipative systems of ordinary differential equations. One often turns to numerical integration to solve them. There is an incompatibility, however, between the answers it can produce (i.e., specific solution trajectories) and the questions one might wish to ask (e.g., what behavior would be typical in the laboratory?) To determine its outcome, numerical integration requires more detailed initial conditions than a laboratory could normally provide. In place of initial conditions, experiments stipulate how tests should be carried out: only under statistically stationary conditions, for example, or only during asymptotic approach to a final state. Stipulations such as these, rather than initial conditions, are what determine outcomes in the laboratory.This theoretical study examines whether the points of view can be reconciled: What is the relationship between one's statistical stipulations for how an experiment should be carried out--stationarity or asymptotic approach--and the expected results? How might those results be determined without invoking initial conditions explicitly?To answer these questions, stationarity and asymptotic approach conditions are analyzed in detail. Each condition is treated as a statistical constraint on the system--a restriction on the probability density of states that might be occupied when measurements take place. For stationarity, this reasoning leads to a singular, invariant probability density which is already familiar from dynamical systems theory. For asymptotic approach, it leads to a new, more regular probability density field. A conjecture regarding what appears to be a limit relationship between the two densities is presented.By making use of the new probability densities, one can derive output statistics directly, avoiding the need to create or manipulate initial data, and thereby avoiding the conceptual incompatibility mentioned above. This approach also provides a clean way to derive reduced-order models, complete with local and global error estimates, as well as a way to compare existing reduced-order models objectively.The new approach is explored in the context of five separate test problems: a trivial one-dimensional linear system, a damped unforced linear oscillator in two dimensions, the isothermal Rayleigh-Plesset equation, Lorenz's equations, and the Stokes limit of Burgers' equation in one space dimension. In each case, various output statistics are deduced without recourse to initial conditions. Further, reduced-order models are constructed for asymptotic approach of the damped unforced linear oscillator, the isothermal Rayleigh-Plesset system, and Lorenz's equations, and for stationarity of Lorenz's equations.

Evolutionary Epistemology and the Educative Process.

ERIC Educational Resources Information Center

Perkinson, Henry J.

2003-01-01

Uses Karl Popper's theory that knowledge is produced through continual trial conjectures and error elimination to argue that students are fallible creators of knowledge and that the primary role of the teacher is as a critic. (EV)

Some General Thoughts about Broken Symmetry.

DTIC Science & Technology

1981-01-21

to what extent one may generalize to random systems and to ’dissipative structures’. Thermal equilibrium broken symmetry is characterized by an order...stable defects. We conjecture what may be the consequences of relaxing these assumptions. (Author)

A Fallibilistic Model for Instruction

ERIC Educational Resources Information Center

Dawson, A. J.

1971-01-01

Discusses models in inquiry and of instruction based on critical Fallibilistic philosophy, developed by Karl R. Popper, which holds that all knowledge grows by conjecture and refutation. Classroom applications of strategies which result from the model are presented. (JP)

Shapes of the Future

ERIC Educational Resources Information Center

Klee, Victor

1971-01-01

This article presents some easily stated but unsolved geometric problems. The three sections are entitled: Housemoving, Manholes and Fermi Surfaces" (convex figures of constant width), Angels, Pollen Grains and Misanthropes" (packing problems), and The Four-Color Conjecture and Organic Chemistry." (MM)

Noncommutative Field Theories and (super)string Field Theories

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Belov, D. M.; Giryavets, A. A.; Koshelev, A. S.; Medvedev, P. B.

2002-11-01

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, "comma" and matrix representations of vertices.

Cluster Correspondence Analysis.

PubMed

van de Velden, M; D'Enza, A Iodice; Palumbo, F

2017-03-01

A method is proposed that combines dimension reduction and cluster analysis for categorical data by simultaneously assigning individuals to clusters and optimal scaling values to categories in such a way that a single between variance maximization objective is achieved. In a unified framework, a brief review of alternative methods is provided and we show that the proposed method is equivalent to GROUPALS applied to categorical data. Performance of the methods is appraised by means of a simulation study. The results of the joint dimension reduction and clustering methods are compared with the so-called tandem approach, a sequential analysis of dimension reduction followed by cluster analysis. The tandem approach is conjectured to perform worse when variables are added that are unrelated to the cluster structure. Our simulation study confirms this conjecture. Moreover, the results of the simulation study indicate that the proposed method also consistently outperforms alternative joint dimension reduction and clustering methods.

Small instanton transitions for M5 fractions

NASA Astrophysics Data System (ADS)

Mekareeya, Noppadol; Ohmori, Kantaro; Shimizu, Hiroyuki; Tomasiello, Alessandro

2017-10-01

M5-branes on an ADE singularity are described by certain six-dimensional "conformal matter" superconformal field theories. Their Higgs moduli spaces contain information about various dynamical processes for the M5s; however, they are not directly accessible due to the lack of a Lagrangian formulation. Using anomaly matching, we compute their dimensions. The result implies that M5 fractions can recombine in several different ways, where the M5s are leaving behind frozen versions of the singularity. The anomaly polynomial gives hints about the nature of the freezing. We also check the Higgs dimension formula by comparing it with various existing conjectures for the CFTs one obtains by torus compactifications down to four and three dimensions. Aided by our results, we also extend those conjectures to compactifications of theories not previously considered. These involve class S theories with twisted punctures in four dimensions, and affine-Dynkin-shaped quivers in three dimensions.

Abnormal characteristics of binary molecular clusters in DMSO–ethanol mixtures under external electric fields

NASA Astrophysics Data System (ADS)

Wu, Zhiyan; Huang, Kama

2018-05-01

For the nonlinearly phenomena on the dielectric properties of dimethyl sulfoxide (DMSO)-ethanol mixtures under a low intensity microwave field, we propose a conjecture that there exist some abnormal molecular clusters. To interpret the mechanism of abnormal phenomena and confirm our conjecture about the existence of abnormal molecular clusters, an in-depth investigation about the structure evolutions of (DMSO)m(C2H5OH)n (m = 0-4; n = 0-4; m + n ≤ 4) molecular clusters induced by external electric fields has been given by using density functional theory. The results show that there exist some binary molecular clusters with large cluster radii in mixtures, and some of them are unstable under exposure of electric fields. It implies that the existence of certain abnormal molecular clusters in DMSO-ethanol mixtures results in their abnormality of dielectric properties.

Refined open intersection numbers and the Kontsevich-Penner matrix model

NASA Astrophysics Data System (ADS)

Alexandrov, Alexander; Buryak, Alexandr; Tessler, Ran J.

2017-03-01

A study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J.P. Solomon and the third author, where they introduced open intersection numbers in genus 0. Their construction was later generalized to all genera by J.P. Solomon and the third author. In this paper we consider a refinement of the open intersection numbers by distinguishing contributions from surfaces with different numbers of boundary components, and we calculate all these numbers. We then construct a matrix model for the generating series of the refined open intersection numbers and conjecture that it is equivalent to the Kontsevich-Penner matrix model. An evidence for the conjecture is presented. Another refinement of the open intersection numbers, which describes the distribution of the boundary marked points on the boundary components, is also discussed.

Schottky's conjecture on multiplication of field enhancement factors

NASA Astrophysics Data System (ADS)

Miller, Ryan; Lau, Y. Y.; Booske, John H.

2009-11-01

Of great interest to high power microwave, millimeter wave to terahertz sources, x-ray tubes, electrons guns, etc., is the electric field enhancement obtained from sharp emitting structures fabricated by various microfabrication methods. In this paper, we use conformal mapping to investigate the field enhancement of several rectilinear geometries, including a single rectangular ridge, a trapezoidal ridge, and their superposition, i.e., one ridge on top of another. We show that the composite field enhancement factor of the double ridge with a microprotrusion on top of a macroprotrusion is dominated by the product of the individual protrusions' field enhancement factors over a very wide range of geometric aspect ratios, as conjectured by Schottky. Simplified scaling laws are proposed. Significant deviation from Schottky's product rule occurs almost exclusively when the half-width of the macroprotrusion is less than the height of the microprotrusion. Accurate expressions of the divergent electric field near the sharp edges are derived.

ER = EPR and non-perturbative action integrals for quantum gravity

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina

In this paper, we construct and calculate non-perturbative path integrals in a multiply-connected spacetime. This is done by summing over homotopy classes of paths. The topology of the spacetime is defined by Einstein-Rosen bridges (ERB) forming from the entanglement of quantum foam described by virtual black holes. As these “bubbles” are entangled, they are connected by Planckian ERBs because of the ER = EPR conjecture. Hence, the spacetime will possess a large first Betti number B1. For any compact 2-surface in the spacetime, the topology (in particular the homotopy) of that surface is non-trivial due to the large number of Planckian ERBs that define homotopy through this surface. The quantization of spacetime with this topology — along with the proper choice of the 2-surfaces — is conjectured to allow non-perturbative path integrals of quantum gravity theory over the spacetime manifold.

Flat monodromies and a Moduli Space Size Conjecture

NASA Astrophysics Data System (ADS)

Hebecker, Arthur; Henkenjohann, Philipp; Witkowski, Lukas T.

2017-12-01

We investigate how super-Planckian axions can arise when type IIB 3-form flux is used to restrict a two-axion field space to a one-dimensional winding trajectory. If one does not attempt to address notoriously complicated issues like Kähler moduli stabilization, SUSY-breaking and inflation, this can be done very explicitly. We show that the presence of flux generates flat monodromies in the moduli space which we therefore call `Monodromic Moduli Space'. While we do indeed find long axionic trajectories, these are non-geodesic. Moreover, the length of geodesics remains highly constrained, in spite of the (finite) monodromy group introduced by the flux. We attempt to formulate this in terms of a `Moduli Space Size Conjecture'. Interesting mathematical structures arise in that the relevant spaces turn out to be fundamental domains of congruence subgroups of the modular group. In addition, new perspectives on inflation in string theory emerge.

Weak cosmic censorship: as strong as ever.

PubMed

Hod, Shahar

2008-03-28

Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the most important open questions in general relativity. In this Letter, we reanalyze extreme situations which have been considered as counterexamples to the weak cosmic censorship conjecture. In particular, we consider the absorption of scalar particles with large angular momentum by a black hole. Ignoring back reaction effects may lead one to conclude that the incident wave may overspin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when back reaction effects are properly taken into account, the stability of the black-hole event horizon is irrefutable. We therefore conclude that cosmic censorship is actually respected in this type of gedanken experiments.

The bulk, surface and corner free energies of the square lattice Ising model

NASA Astrophysics Data System (ADS)

Baxter, R. J.

2017-01-01

We use Kaufman’s spinor method to calculate the bulk, surface and corner free energies {f}{{b}},{f}{{s}},{f}{{s}}\\prime ,{f}{{c}} of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For {f}{{b}},{f}{{s}},{f}{{s}}\\prime our results of course agree with the early work of Onsager, McCoy and Wu. We also find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic case. We note that the corner free energy f c depends only on the elliptic modulus k that enters the working, and not on the argument v, which means that VJ’s conjecture applies for the full anisotropic model. The only aspect of this paper that is new is the actual derivation of f c, but by reporting all four free energies together we can see interesting structures linking them.

Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert-Kolmogorov Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits

NASA Astrophysics Data System (ADS)

Leonov, G. A.; Kuznetsov, N. V.

From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect with small neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure. For localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. At first, the problem of investigating hidden oscillations arose in the second part of Hilbert's 16th problem (1900). The first nontrivial results were obtained in Bautin's works, which were devoted to constructing nested limit cycles in quadratic systems, that showed the necessity of studying hidden oscillations for solving this problem. Later, the problem of analyzing hidden oscillations arose from engineering problems in automatic control. In the 50-60s of the last century, the investigations of widely known Markus-Yamabe's, Aizerman's, and Kalman's conjectures on absolute stability have led to the finding of hidden oscillations in automatic control systems with a unique stable stationary point. In 1961, Gubar revealed a gap in Kapranov's work on phase locked-loops (PLL) and showed the possibility of the existence of hidden oscillations in PLL. At the end of the last century, the difficulties in analyzing hidden oscillations arose in simulations of drilling systems and aircraft's control systems (anti-windup) which caused crashes. Further investigations on hidden oscillations were greatly encouraged by the present authors' discovery, in 2010 (for the first time), of chaotic hidden attractor in Chua's circuit. This survey is dedicated to efficient analytical-numerical methods for the study of hidden oscillations. Here, an attempt is made to reflect the current trends in the synthesis of analytical and numerical methods.

Cluster-cluster aggregation kinetics and primary particle growth of soot nanoparticles in flame by light scattering and numerical simulations.

PubMed

di Stasio, Stefano; Konstandopoulos, Athanasios G; Kostoglou, Margaritis

2002-03-01

The agglomeration kinetics of growing soot generated in a diffusion atmospheric flame are here studied in situ by light scattering technique to infer cluster morphology and size (fractal dimension D(f) and radius of gyration R(g)). SEM analysis is used as a standard reference to obtain primary particle size D(P) at different residence times. The number N(P) of primary particles per aggregate and the number concentration n(A) of clusters are evaluated on the basis of the measured angular patterns of the scattered light intensity. The major finding is that the kinetics of the coagulation process that yields to the formation of chain-like aggregates by soot primary particles (size 10 to 40 nm) can be described with a constant coagulation kernel beta(c,exp)=2.37x10(-9) cm3/s (coagulation constant tau(c) approximately = 0.28 ms). This result is in nice accord with the Smoluchowski coagulation equation in the free molecular regime, and, vice versa, it is in contrast with previous studies conducted by invasive (ex situ) techniques, which claimed the evidence in flames of coagulation rates much larger than the kinetic theory predictions. Thereafter, a number of numerical simulations is implemented to compare with the experimental results on primary particle growth rate and on the process of aggregate reshaping that is observed by light scattering at later residence times. The restructuring process is conjectured to occur, for not well understood reasons, as a direct consequence of the atomic rearrangement in the solid phase carbon due to the prolonged residence time within the flame. Thus, on one side, it is shown that the numerical simulations of primary size history compare well with the values of primary size from SEM experiment with a growth rate constant of primary diameter about 1 nm/s. On the other side, the evolution of aggregate morphology is found to be predictable by the numerical simulations when the onset of a first-order "thermal" restructuring mechanism is assumed to occur in the flame at about 20 ms residence time leading to aggregates with an asymptotic fractal dimension D(f,infinity) approximately = 2.5.

Connections between Kac-Moody algebras and M-theory

NASA Astrophysics Data System (ADS)

Cook, Paul P.

2007-11-01

We investigate some of the motivations and consequences of the conjecture that the Kac-Moody algebra E11 is the symmetry algebra of M-theory, and we develop methods to aid the further investigation of this idea. The definitions required to work with abstract root systems of Lie algebras are given in review leading up to the definition of a Kac-Moody algebra. The motivations for the E11 conjecture are presented and the nonlinear realisation of gravity relevant to the conjecture is described. We give a beginner's guide to producing the algebras of E11, relevant to M-theory, and K27, relevant to the bosonic string theory, along with their l1 representations are constructed. Reference tables of low level roots are produced for both the adjoint and l1 representations of these algebras. In addition a particular group element, having a generic form for all G+++ algebras, is shown to encode all the half-BPS brane solutions of the maximally oxidised supergravities. Special analysis is given to the role of space-time signature in the context of this group element and subsequent to this analysis spacelike brane solutions are derived from the same solution generating group element. Finally the appearance of U-duality charge multiplets from E11 is reviewed. General formulae for finding the content of arbitrary brane charge multiplets are given and the content of the particle and string multiplets in dimensions 4,5,6,7 and 8 is shown to be contained in the l1 representation of E11.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Elliptic integral evaluations of Bessel moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2008-01-06

We record what is known about the closed forms for variousBessel function moments arising in quantum field theory, condensed mattertheory and other parts of mathematical physics. More generally, wedevelop formulae for integrals of products of six or fewer Besselfunctions. In consequence, we are able to discover and prove closed formsfor c(n,k) := Int_0 inf tk K_0 n(t) dt, with integers n = 1, 2, 3, 4 andk greater than or equal to 0, obtaining new results for the even momentsc3,2k and c4,2k . We also derive new closed forms for the odd momentss(n,2k+1) := Int_0 inf t(2k+1) I_0(t) K_0n(t) dt,withmore » n = 3, 4 and fort(n,2k+1) := Int_0 inf t(2k+1) I_02(t) K_0(n-2) dt, with n = 5, relatingthe latter to Green functions on hexagonal, diamond and cubic lattices.We conjecture the values of s(5,2k+1), make substantial progress on theevaluation of c(5,2k+1), s(6,2k+1) and t(6,2k+1) and report more limitedprogress regarding c(5,2k), c(6,2k+1) and c(6,2k). In the process, weobtain 8 conjectural evaluations, each of which has been checked to 1200decimal places. One of these lies deep in 4-dimensional quantum fieldtheory and two are probably provable by delicate combinatorics. Thereremains a hard core of five conjectures whose proofs would be mostinstructive, to mathematicians and physicists alike.« less

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

The impact of skull bone intensity on the quality of compressed CT neuro images

NASA Astrophysics Data System (ADS)

Kowalik-Urbaniak, Ilona; Vrscay, Edward R.; Wang, Zhou; Cavaro-Menard, Christine; Koff, David; Wallace, Bill; Obara, Boguslaw

2012-02-01

The increasing use of technologies such as CT and MRI, along with a continuing improvement in their resolution, has contributed to the explosive growth of digital image data being generated. Medical communities around the world have recognized the need for efficient storage, transmission and display of medical images. For example, the Canadian Association of Radiologists (CAR) has recommended compression ratios for various modalities and anatomical regions to be employed by lossy JPEG and JPEG2000 compression in order to preserve diagnostic quality. Here we investigate the effects of the sharp skull edges present in CT neuro images on JPEG and JPEG2000 lossy compression. We conjecture that this atypical effect is caused by the sharp edges between the skull bone and the background regions as well as between the skull bone and the interior regions. These strong edges create large wavelet coefficients that consume an unnecessarily large number of bits in JPEG2000 compression because of its bitplane coding scheme, and thus result in reduced quality at the interior region, which contains most diagnostic information in the image. To validate the conjecture, we investigate a segmentation based compression algorithm based on simple thresholding and morphological operators. As expected, quality is improved in terms of PSNR as well as the structural similarity (SSIM) image quality measure, and its multiscale (MS-SSIM) and informationweighted (IW-SSIM) versions. This study not only supports our conjecture, but also provides a solution to improve the performance of JPEG and JPEG2000 compression for specific types of CT images.

Concerted evolution of life stage performances signals recent selection on yeast nitrogen use.

PubMed

Ibstedt, Sebastian; Stenberg, Simon; Bagés, Sara; Gjuvsland, Arne B; Salinas, Francisco; Kourtchenko, Olga; Samy, Jeevan K A; Blomberg, Anders; Omholt, Stig W; Liti, Gianni; Beltran, Gemma; Warringer, Jonas

2015-01-01

Exposing natural selection driving phenotypic and genotypic adaptive differentiation is an extraordinary challenge. Given that an organism's life stages are exposed to the same environmental variations, we reasoned that fitness components, such as the lag, rate, and efficiency of growth, directly reflecting performance in these life stages, should often be selected in concert. We therefore conjectured that correlations between fitness components over natural isolates, in a particular environmental context, would constitute a robust signal of recent selection. Critically, this test for selection requires fitness components to be determined by different genetic loci. To explore our conjecture, we exhaustively evaluated the lag, rate, and efficiency of asexual population growth of natural isolates of the model yeast Saccharomyces cerevisiae in a large variety of nitrogen-limited environments. Overall, fitness components were well correlated under nitrogen restriction. Yeast isolates were further crossed in all pairwise combinations and coinheritance of each fitness component and genetic markers were traced. Trait variations tended to map to quantitative trait loci (QTL) that were private to a single fitness component. We further traced QTLs down to single-nucleotide resolution and uncovered loss-of-function mutations in RIM15, PUT4, DAL1, and DAL4 as the genetic basis for nitrogen source use variations. Effects of SNPs were unique for a single fitness component, strongly arguing against pleiotropy between lag, rate, and efficiency of reproduction under nitrogen restriction. The strong correlations between life stage performances that cannot be explained by pleiotropy compellingly support adaptive differentiation of yeast nitrogen source use and suggest a generic approach for detecting selection. © The Author 2014. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

THE POSSIBLE ROLE OF CORONAL STREAMERS AS MAGNETICALLY CLOSED STRUCTURES IN SHOCK-INDUCED ENERGETIC ELECTRONS AND METRIC TYPE II RADIO BURSTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kong, Xiangliang; Chen, Yao; Feng, Shiwei

2015-01-10

Two solar type II radio bursts, separated by ∼24 hr in time, are examined together. Both events are associated with coronal mass ejections (CMEs) erupting from the same active region (NOAA 11176) beneath a well-observed helmet streamer. We find that the type II emissions in both events ended once the CME/shock fronts passed the white-light streamer tip, which is presumably the magnetic cusp of the streamer. This leads us to conjecture that the closed magnetic arcades of the streamer may play a role in electron acceleration and type II excitation at coronal shocks. To examine such a conjecture, we conduct a test-particle simulationmore » for electron dynamics within a large-scale partially closed streamer magnetic configuration swept by a coronal shock. We find that the closed field lines play the role of an electron trap via which the electrons are sent back to the shock front multiple times and therefore accelerated to high energies by the shock. Electrons with an initial energy of 300 eV can be accelerated to tens of keV concentrating at the loop apex close to the shock front with a counter-streaming distribution at most locations. These electrons are energetic enough to excite Langmuir waves and radio bursts. Considering the fact that most solar eruptions originate from closed field regions, we suggest that the scenario may be important for the generation of more metric type IIs. This study also provides an explanation of the general ending frequencies of metric type IIs at or above 20-30 MHz and the disconnection issue between metric and interplanetary type IIs.« less

Resting state functional connectivity of the ventral auditory pathway in musicians with absolute pitch.

PubMed

Kim, Seung-Goo; Knösche, Thomas R

2017-08-01

Absolute pitch (AP) is the ability to recognize pitch chroma of tonal sound without external references, providing a unique model of the human auditory system (Zatorre: Nat Neurosci 6 () 692-695). In a previous study (Kim and Knösche: Hum Brain Mapp () 3486-3501), we identified enhanced intracortical myelination in the right planum polare (PP) in musicians with AP, which could be a potential site for perceptional processing of pitch chroma information. We speculated that this area, which initiates the ventral auditory pathway, might be crucially involved in the perceptual stage of the AP process in the context of the "dual pathway hypothesis" that suggests the role of the ventral pathway in processing nonspatial information related to the identity of an auditory object (Rauschecker: Eur J Neurosci 41 () 579-585). To test our conjecture on the ventral pathway, we investigated resting state functional connectivity (RSFC) using functional magnetic resonance imaging (fMRI) from musicians with varying degrees of AP. Should our hypothesis be correct, RSFC via the ventral pathway is expected to be stronger in musicians with AP, whereas such group effect is not predicted in the RSFC via the dorsal pathway. In the current data, we found greater RSFC between the right PP and bilateral anteroventral auditory cortices in musicians with AP. In contrast, we did not find any group difference in the RSFC of the planum temporale (PT) between musicians with and without AP. We believe that these findings support our conjecture on the critical role of the ventral pathway in AP recognition. Hum Brain Mapp 38:3899-3916, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Exact deconstruction of the 6D (2,0) theory

NASA Astrophysics Data System (ADS)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodríguez-Gómez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

A cluster analysis investigation of workaholism as a syndrome.

PubMed

Aziz, Shahnaz; Zickar, Michael J

2006-01-01

Workaholism has been conceptualized as a syndrome although there have been few tests that explicitly consider its syndrome status. The authors analyzed a three-dimensional scale of workaholism developed by Spence and Robbins (1992) using cluster analysis. The authors identified three clusters of individuals, one of which corresponded to Spence and Robbins's profile of the workaholic (high work involvement, high drive to work, low work enjoyment). Consistent with previously conjectured relations with workaholism, individuals in the workaholic cluster were more likely to label themselves as workaholics, more likely to have acquaintances label them as workaholics, and more likely to have lower life satisfaction and higher work-life imbalance. The importance of considering workaholism as a syndrome and the implications for effective interventions are discussed. Copyright 2006 APA.

B(H) has a pure state that is not multiplicative on any masa.

PubMed

Akemann, Charles; Weaver, Nik

2008-04-08

Assuming the continuum hypothesis, we prove that Bernoulli function(H) has a pure state whose restriction to any masa is not pure. This resolves negatively old conjectures of Kadison and Singer and of Anderson.

Raiders of the Latest Art: American Treasure Trove.

ERIC Educational Resources Information Center

May, Mary Jo

1986-01-01

Lists writing exercises based on observations students can make in a shopping mall. Notes that the exercises are intended to become a springboard for study, description, conjecture, evidence, example, and innovation, and can be combined, expanded, or shortened. (EL)

1963 Vajont rock slide: a comparison between 3D DEM and 3D FEM

NASA Astrophysics Data System (ADS)

Crosta, Giovanni; Utili, Stefano; Castellanza, Riccardo; Agliardi, Federico; Bistacchi, Andrea; Weng Boon, Chia

2013-04-01

Data on the exact location of the failure surface of the landslide have been used as the starting point for the modelling of the landslide. 3 dimensional numerical analyses were run employing both the discrete element method (DEM) and a Finite Element Method (FEM) code. In this work the focus is on the prediction of the movement of the landlside during its initial phase of detachment from Mount Toc. The results obtained by the two methods are compared and conjectures on the observed discrepancies of the predictions between the two methods are formulated. In the DEM simulations the internal interaction of the sliding blocks and the expansion of the debris is obtained as a result of the kinematic interaction among the rock blocks resulting from the jointing of the rock mass involved in the slide. In the FEM analyses, the c-phi reduction technique was employed along the predefine failure surface until the onset of the landslide occurred. In particular, two major blocks of the landslide were identified and the stress, strain and displacement fields at the interface between the two blocks were analysed in detail.

Games of age-dependent prevention of chronic infections by social distancing.

PubMed

Reluga, Timothy C; Li, Jing

2013-06-01

Epidemiological games combine epidemic modelling with game theory to assess strategic choices in response to risks from infectious diseases. In most epidemiological games studied thus-far, the strategies of an individual are represented with a single choice parameter. There are many natural situations where strategies can not be represented by a single dimension, including situations where individuals can change their behavior as they age. To better understand how age-dependent variations in behavior can help individuals deal with infection risks, we study an epidemiological game in an SI model with two life-history stages where social distancing behaviors that reduce exposure rates are age-dependent. When considering a special case of the general model, we show that there is a unique Nash equilibrium when the infection pressure is a monotone function of aggregate exposure rates, but non-monotone effects can appear even in our special case. The non-monotone effects sometimes result in three Nash equilibria, two of which have local invasion potential simultaneously. Returning to a general case, we also describe a game with continuous age-structure using partial-differential equations, numerically identify some Nash equilibria, and conjecture about uniqueness.

PROPERTIES AND MODELING OF UNRESOLVED FINE STRUCTURE LOOPS OBSERVED IN THE SOLAR TRANSITION REGION BY IRIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brooks, David H.; Reep, Jeffrey W.; Warren, Harry P.

Recent observations from the Interface Region Imaging Spectrograph ( IRIS ) have discovered a new class of numerous low-lying dynamic loop structures, and it has been argued that they are the long-postulated unresolved fine structures (UFSs) that dominate the emission of the solar transition region. In this letter, we combine IRIS measurements of the properties of a sample of 108 UFSs (intensities, lengths, widths, lifetimes) with one-dimensional non-equilibrium ionization simulations, using the HYDRAD hydrodynamic model to examine whether the UFSs are now truly spatially resolved in the sense of being individual structures rather than being composed of multiple magnetic threads.more » We find that a simulation of an impulsively heated single strand can reproduce most of the observed properties, suggesting that the UFSs may be resolved, and the distribution of UFS widths implies that they are structured on a spatial scale of 133 km on average. Spatial scales of a few hundred kilometers appear to be typical for a range of chromospheric and coronal structures, and we conjecture that this could be an important clue for understanding the coronal heating process.« less

Exact quantum numbers of collapsed and non-collapsed two-string solutions in the spin-1/2 Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Deguchi, Tetsuo; Ranjan Giri, Pulak

2016-04-01

Every solution of the Bethe-ansatz equations (BAEs) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For the spin-1/2 XXX chain we rigorously derive all the quantum numbers for the complete set of the Bethe-ansatz eigenvectors in the two down-spin sector with any chain length N. Here we obtain them both for real and complex solutions. We also show that all the solutions associated with them are distinct. Consequently, we prove the completeness of the Bethe ansatz and give an exact expression for the number of real solutions which correspond to collapsed bound-state solutions (i.e., two-string solutions) in the sector: 2[(N-1)/2-(N/π ){{tan}}-1(\\sqrt{N-1})] in terms of Gauss’ symbol. Moreover, we prove in the sector the scheme conjectured by Takahashi for solving BAE systematically. We also suggest that by applying the present method we can derive the quantum numbers for the spin-1/2 XXZ chain.

Universality, maximum radiation, and absorption in high-energy collisions of black holes with spin.

PubMed

Sperhake, Ulrich; Berti, Emanuele; Cardoso, Vitor; Pretorius, Frans

2013-07-26

We explore the impact of black hole spins on the dynamics of high-energy black hole collisions. We report results from numerical simulations with γ factors up to 2.49 and dimensionless spin parameter χ=+0.85, +0.6, 0, -0.6, -0.85. We find that the scattering threshold becomes independent of spin at large center-of-mass energies, confirming previous conjectures that structure does not matter in ultrarelativistic collisions. It has further been argued that in this limit all of the kinetic energy of the system may be radiated by fine tuning the impact parameter to threshold. On the contrary, we find that only about 60% of the kinetic energy is radiated for γ=2.49. By monitoring apparent horizons before and after scattering events we show that the "missing energy" is absorbed by the individual black holes in the encounter, and moreover the individual black-hole spins change significantly. We support this conclusion with perturbative calculations. An extrapolation of our results to the limit γ→∞ suggests that about half of the center-of-mass energy of the system can be emitted in gravitational radiation, while the rest must be converted into rest-mass and spin energy.

The simplicial Ricci tensor

NASA Astrophysics Data System (ADS)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

A hydrodynamic mechanism for spontaneous formation of ordered drop arrays in confined shear flow

NASA Astrophysics Data System (ADS)

Singha, Sagnik; Zurita-Gotor, Mauricio; Loewenberg, Michael; Migler, Kalman; Blawzdziewicz, Jerzy

2017-11-01

It has been experimentally demonstrated that a drop monolayer driven by a confined shear flow in a Couette device can spontaneously arrange into a flow-oriented parallel chain microstructure. However, the hydrodynamic mechanism of this puzzling self-assembly phenomenon has so far eluded explanation. In a recent publication we suggested that the observed spontaneous drop ordering may arise from hydrodynamic interparticle interactions via a far-field quadrupolar Hele-Shaw flow associated with drop deformation. To verify this conjecture we have developed a simple numerical-simulation model that includes the far-field Hele-Shaw flow quadrupoles and a near-field short-range repulsion. Our simulations show that an initially disordered particle configuration self-organizes into a system of particle chains, similar to the experimentally observed drop-chain structures. The initial stage of chain formation is fast; subsequently, microstructural defects in a partially ordered system are removed by slow annealing, leading to an array of equally spaced parallel chains with a small number of defects. The microstructure evolution is analyzed using angular and spatial order parameters and correlation functions. Supported by NSF Grants No. CBET 1603627 and CBET 1603806.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costigliola, Lorenzo; Schrøder, Thomas B.; Dyre, Jeppe C.

The recent theoretical prediction by Maimbourg and Kurchan [e-print http://arxiv.org/abs/1603.05023 (2016)] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension d goes to infinity is investigated for the standard 12-6 Lennard-Jones fluid. This is done by computer simulations for d = 2, 3, 4 going from the critical point along the critical isotherm/isochore to higher density/temperature. In both cases the virial potential-energy correlation coefficient increases significantly. For a given density and temperature relative to the critical point, with increasing number of dimension the Lennard-Jones system conforms better to the hidden-scale-invariance property characterized bymore » high virial potential-energy correlations (a property that leads to the existence of isomorphs in the thermodynamic phase diagram, implying that it becomes effectively one-dimensional in regard to structure and dynamics). The present paper also gives the first numerical demonstration of isomorph invariance of structure and dynamics in four dimensions. Our findings emphasize the need for a universally applicable 1/d expansion in liquid-state theory; we conjecture that the systems known to obey hidden scale invariance in three dimensions are those for which the yet-to-be-developed 1/d expansion converges rapidly.« less

On the behavior of the leading eigenvalue of Eigen's evolutionary matrices.

PubMed

Semenov, Yuri S; Bratus, Alexander S; Novozhilov, Artem S

2014-12-01

We study general properties of the leading eigenvalue w¯(q) of Eigen's evolutionary matrices depending on the replication fidelity q. This is a linear algebra problem that has various applications in theoretical biology, including such diverse fields as the origin of life, evolution of cancer progression, and virus evolution. We present the exact expressions for w¯(q),w¯(')(q),w¯('')(q) for q = 0, 0.5, 1 and prove that the absolute minimum of w¯(q), which always exists, belongs to the interval (0, 0.5]. For the specific case of a single peaked landscape we also find lower and upper bounds on w¯(q), which are used to estimate the critical mutation rate, after which the distribution of the types of individuals in the population becomes almost uniform. This estimate is used as a starting point to conjecture another estimate, valid for any fitness landscape, and which is checked by numerical calculations. The last estimate stresses the fact that the inverse dependence of the critical mutation rate on the sequence length is not a generally valid fact. Copyright © 2014 Elsevier Inc. All rights reserved.

Topics in Gravitation and Cosmology

NASA Astrophysics Data System (ADS)

Bahrami Taghanaki, Sina

This thesis is focused on two topics in which relativistic gravitational fields play an important role, namely early Universe cosmology and black hole physics. The theory of cosmic inflation has emerged as the most successful theory of the very early Universe with concrete and verifiable predictions for the properties of anisotropies of the cosmic microwave background radiation and large scale structure. Coalescences of black hole binaries have recently been detected by the Laser Interferometer Gravitational Wave Observatory (LIGO), opening a new arena for observationally testing the dynamics of gravity. In part I of this thesis we explore some modifications to the standard theory of inflation. The main predictions of single field slow-roll inflation have been largely consistent with cosmological observations. However, there remain some aspects of the theory that are not presently well understood. Among these are the somewhat interrelated issues of the choice of initial state for perturbations and the potential imprints of pre-inflationary dynamics. It is well known that a key prediction of the standard theory of inflation, namely the Gaussianity of perturbations, is a consequence of choosing a natural vacuum initial state. In chapter 3, we study the generation and detectability of non-Gaussianities in inflationary scalar perturbations that originate from more general choices of initial state. After that, in chapter 4, we study a simple but predictive model of pre-inflationary dynamics in an attempt to test the robustness of inflationary predictions. We find that significant deviations from the standard predictions are unlikely to result from models in which the inflaton field decouples from the pre-inflationary degrees of freedom prior to freeze-out of the observable modes. In part II we turn to a study of an aspect of the thermodynamics of black holes, a subject which has led to important advances in our understanding of quantum gravity. For objects which collapse to form black holes, we examine a conjectured relationship between the objects' entropy, the collapse timescale, and the mass of the final black hole. This relationship is relevant for understanding the nature of generic quantum mechanical states of black hole interiors. In chapter 6 we construct a counter-example to a weak version of the conjectured relation.

Teachers' Interpretations of Student Statements about Slope

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah; Styers, Jodie L.

2017-01-01

This paper describes seven in-service teachers' interpretations of student statements about slope. The teachers interpreted sample student work, conjectured about student contributions, assessed the students' understanding, and positioned the students' statements in the mathematics curriculum. The teachers' responses provide insight into their…

Mesopotamia, A Difficult but Interesting Topic.

ERIC Educational Resources Information Center

Kavett, Hyman

1979-01-01

Describes a method to help students become participants in historical analysis rather than observers of ancient history. Mesopotamia is used as a case study of a culture for which opportunities exist for conjecture, hypothesis formation, research, extrapolation, problem solving, and statements of causality. (Author/DB)

Mysterious Subtractions

ERIC Educational Resources Information Center

Hillen, Amy F.; Watanabe, Tad

2013-01-01

Recent documents suggest that all students, even young children, should have opportunities to engage in reasoning and proof (CCSSI 2010; NCTM 2000, 2006, 2009). One mathematical practice that is central to reasoning and proof is making conjectures (CCSSI 2010; NCTM 2000; Stylianides 2008). In the elementary grades, "formulating conjectures…

The robustness of zero-determinant strategies in Iterated Prisoner's Dilemma games.

PubMed

Chen, Jing; Zinger, Aleksey

2014-09-21

Press and Dyson (2012) discovered a special set of strategies in two-player Iterated Prisoner's Dilemma games, the zero-determinant (ZD) strategies. Surprisingly, a player using such strategies can unilaterally enforce a linear relation between the payoffs of the two players. In particular, with a subclass of such strategies, the extortionate strategies, the former player obtains an advantageous share of the total payoff of the players, and the other player׳s best response is to always cooperate, by doing which he maximizes the payoff of the extortioner as well. When an extortionate player faces a player who is not aware of the theory of ZD strategies and improves his own payoff by adaptively changing his strategy following some unknown dynamics, Press and Dyson conjecture that there always exist adapting paths for the latter leading to the maximum possible scores for both players. In this work we confirm their conjecture in a very strong sense, not just for extortionate strategies, but for all ZD strategies that impose positive correlations between the players' payoffs. We show that not only the conjectured adapting paths always exist, but that actually every adapting path leads to the maximum possible scores, although some paths may not lead to the unconditional cooperation by the adapting player. This is true even in the rare cases where the setup of Press and Dyson is not directly applicable. Our result shows that ZD strategies are even more powerful than as pointed out by their discoverers. Given our result, the player using ZD strategies is assured that she will receive the maximum payoff attainable under the desired payoff relation she imposes, without knowing how the other player will evolve. This makes the use of ZD strategies even more desirable for sentient players. Copyright © 2014 Elsevier Ltd. All rights reserved.

Flow to partially penetrating wells in unconfined heterogeneous aquifers: Mean head and interpretation of pumping tests

NASA Astrophysics Data System (ADS)

Dagan, G.; Lessoff, S. C.

2011-06-01

A partially penetrating well of length Lw and radius Rw starts to pump at constant discharge Qw at t = 0 from an unconfined aquifer of thickness D. The aquifer is of random and stationary conductivity characterized by KG (geometric mean), σY2 (log conductivity variance), and I and Iv (the horizontal and vertical integral scales). The flow problem is solved under a few simplifying assumptions commonly adopted in the literature for homogeneous media: Rw/Lw ≪ 1, linearization of the free surface condition, and constant drainable porosity n. Additionally, it is assumed that Rw/I < 1 and Lw/Iv ≫ 1 (to simplify the well boundary conditions) and that a first-order approximation in σY2 (extended to finite σY2 on a conjectural basis) is adopted. The solution is obtained for the mean head field and the associated water table equation. The main result of the analysis is that the flow domain can be divided into three zones for : (1) the neighborhood of the well R ≪ I, where = (Qw/LwKA)h0(R, z, tKefuv/nD), with h0 being the zero-order solution pertaining to a homogeneous and isotropic aquifer, KA being the conductivity arithmetic mean, and Kefuv being the effective vertical conductivity in mean uniform flow, (2) an exterior zone R ⪆ I in which ?H? = (Qw/LwKefuh)h0(R?, z, tKefuv/nD), with Kefuh being the horizontal effective conductivity, and (3) an intermediate zone in which the solution requires a few numerical quadratures, not carried out here. The application to pumping tests reveals that identification of the aquifer parameters for homogeneous and anisotropic aquifers by commonly used methods can be applied for the drawdown measured in an observation well of length Low?Iv (to ensure exchange of space and ensemble head averages) in the second zone in order to identify Kefuh, Kefuv, and n. In contrast, the use of the drawdown in the well (first zone) leads to an overestimation of Kefuh by the factor KA/Kefuh.

Creationism Challenges Geology: A Retreat to the Eighteenth Century.

ERIC Educational Resources Information Center

Eglin, Paula G.; Graham, Mildred W.

1982-01-01

Some contentions of scientific creationism that conflict with accepted principles of geology (catastrophism, fossil records, earth's age, rock formation, second law of thermodynamics) are reviewed, demonstrating that these claims are based not on scientific research or reasonable conjecture but on Biblical references. (Author/DC)

Exploring & Writing Geometry

ERIC Educational Resources Information Center

Sanders, Cathleen V.

2009-01-01

When given opportunities to explore mathematics, make conjectures, and write about what they have discovered, students gain a deeper understanding of this fascinating subject. In this article, the author describes her successful Geometry Portfolio class. In addition to traditional student work, the author frequently added short essay questions or…

Use of limestone screenings in S-5 surface mixes : final report.

DOT National Transportation Integrated Search

1982-01-01

It is often practical to use limestone screenings in non-polishing S-5 surface mixes in some western areas of Virginia. Also, there has been some conjecture that limestone increases the durability of these mixes. Although the fine aggregate usually h...

Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

Embodied Design: Constructing Means for Constructing Meaning

ERIC Educational Resources Information Center

Abrahamson, Dor

2009-01-01

Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even…

Reply.

ERIC Educational Resources Information Center

Feldman, Carol; And Others

1993-01-01

Replies to the commentary by Olson and Salter on an article by Feldman and others, both reported in this issue. Maintains that the evidence does not support Olson's and Salter's conjecture that the source of age-distinctive lexical differences reported in the Feldman study is a simple function of word frequency. (BC)

The Value of Debts and Credits

ERIC Educational Resources Information Center

Akyuz, Didem

2012-01-01

Research has shown that students should be given the opportunity to explore mathematical concepts by building on their knowledge and focusing on mathematical reasoning. When students represent ideas, make conjectures, collaborate with others, and give explanations and arguments, they are using mathematical reasoning (NCTM 2000). Certain teaching…

Using Scaffolding to Scale-up Justifications

ERIC Educational Resources Information Center

James, Carolyn; Casas, Ana; Grant, Douglas

2016-01-01

Open-ended mathematical tasks provide great opportunities for students to engage in authentic mathematical practices, such as conjecturing, generalizing, and justifying. Supporting students in open-ended tasks can be challenging. Appropriate scaffolding of a task has been linked to more opportunities for student learning and better student…

Einstein Up in Smoke

NASA Astrophysics Data System (ADS)

Lisle, John

2016-01-01

Albert Einstein's biographers have not explained why he developed the abdominal aortic aneurysm that led to his death. Early conjectures proposed that it was caused by syphilis, without accurate evidence. The present article gives evidence to the contrary, and argues that the principal cause of Einstein's death was smoking.

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Rodina, Laurentiu; Trnka, Jaroslav

2018-06-01

We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge invariance in just n -1 particles together with minimal power counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on shell, we show in nontrivial examples that gauge invariance and power counting demand a graph structure for singularities. Thus, both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the nonlinear sigma model and Dirac-Born-Infeld by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.

Filtrations on Springer fiber cohomology and Kostka polynomials

NASA Astrophysics Data System (ADS)

Bellamy, Gwyn; Schedler, Travis

2018-03-01

We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers. In particular, this computes the grading on the zeroth Poisson homology of all classical finite W-algebras, as well as the filtration on the zeroth Hochschild homology of all quantum finite W-algebras, and we generalize to all homology degrees. As a consequence, we deduce a conjecture of Proudfoot on symplectic duality, relating in type A the Poisson homology of Slodowy slices to the intersection cohomology of nilpotent orbit closures. In the last section, we give an analogue of our main theorem in the setting of mirabolic D-modules.

Distillation with Sublogarithmic Overhead.

PubMed

Hastings, Matthew B; Haah, Jeongwan

2018-02-02

It has been conjectured that, for any distillation protocol for magic states for the T gate, the number of noisy input magic states required per output magic state at output error rate ε is Ω[log(1/ε)]. We show that this conjecture is false. We find a family of quantum error correcting codes of parameters ⟦∑[under i=w+1][over m](m/i),∑[under i=0][over w](m/i),∑[under i=w+1][over r+1](r+1/i)⟧ for any integers m>2r, r>w≥0, by puncturing quantum Reed-Muller codes. When m>νr, our code admits a transversal logical gate at the νth level of Clifford hierarchy. In a distillation protocol for magic states at the level ν=3 (T gate), the ratio of input to output magic states is O(log^{γ}(1/ε)), where γ=log(n/k)/log(d)<0.678 for some m, r, w. The smallest code in our family for which γ<1 is on ≈2^{58} qubits.

Holographic space and time: Emergent in what sense?

NASA Astrophysics Data System (ADS)

Vistarini, Tiziana

2017-08-01

This paper proposes a metaphysics for holographic duality. In addition to the AdS/CFT correspondence I also consider the dS/CFT conjecture of duality. Both involve non-perturbative string theory and both are exact dualities. But while the AdS/CFT keeps time at the margins of the story, the dS/CFT conjecture gives to time the "space" it deserves by presenting an interesting holographic model of it. My goals in this paper can be summarized in the following way. First, I argue that the formal structure and physical content of the duality do not support the standard philosophical reading of the relation in terms of grounding. Second, I put forward a philosophical scheme mainly extrapolated from the double aspect monism theory. I read holographic duality in this framework as it seems to fit the mathematical and physical structure of the duality smoothly. Inside this framework I propose a notion of spacetime emergence alternative to those ones commonly debated in the AdS/CFT physics and philosophy circles.

S -duality for holographic p -wave superconductors

NASA Astrophysics Data System (ADS)

Gorsky, Alexander; Gubankova, Elena; Meyer, René; Zayakin, Andrey

2017-11-01

We consider the generalization of the S -duality transformation previously investigated in the context of the fractional quantum Hall effect (FQHE) and s -wave superconductivity to p -wave superconductivity in 2 +1 dimensions in the framework of the AdS /CFT correspondence. The vector Cooper condensate transforms under the S -duality action to the pseudovector condensate at the dual side. The 3 +1 -dimensional Einstein-Yang-Mills theory, the holographic dual to p -wave superconductivity, is used to investigate the S -duality action via the AdS /CFT correspondence. It is shown that, in order to implement the duality transformation, chemical potentials on both the electric and magnetic sides of the duality have to be introduced. A relation for the product of the non-Abelian conductivities in the dual models is derived. We also conjecture a flavor S -duality transformation in the holographic dual to 3 +1 -dimensional QCD low-energy QCD with non-Abelian flavor gauge groups. The conjectured S -duality interchanges isospin and baryonic chemical potentials.

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

DOE PAGES

Song, Jaewon

2016-02-05

We present superconformal indices of 4d N = 2 class S theories with certain irregular punctures called type I k,N. This class of theories include generalized Argyres-Douglas theories of type (A k-1, A N-1) and more. We conjecture the superconformal indices in certain simplifi ed limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture I k,N. We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index andmore » the Macdonald index for odd N. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the (A 1,A 2n) theory. In addition, we discuss the mixed Schur indices for the N = 1 class S theories with irregular punctures.« less

Three applications of a bonus relation for gravity amplitudes

NASA Astrophysics Data System (ADS)

Spradlin, Marcus; Volovich, Anastasia; Wen, Congkao

2009-04-01

Arkani-Hamed et al. have recently shown that all tree-level scattering amplitudes in maximal supergravity exhibit exceptionally soft behavior when two supermomenta are taken to infinity in a particular complex direction, and that this behavior implies new non-trivial relations amongst amplitudes in addition to the well-known on-shell recursion relations. We consider the application of these new 'bonus relations' to MHV amplitudes, showing that they can be used quite generally to relate (n - 2) !-term formulas typically obtained from recursion relations to (n - 3) !-term formulas related to the original BGK conjecture. Specifically we provide (1) a direct proof of a formula presented by Elvang and Freedman, (2) a new formula based on one due to Bedford et al., and (3) an alternate proof of a formula recently obtained by Mason and Skinner. Our results also provide the first direct proof that the conjectured BGK formula, only very recently proven via completely different methods, satisfies the on-shell recursion.

Detection of laryngeal function using speech and electroglottographic data.

PubMed

Childers, D G; Bae, K S

1992-01-01

The purpose of this research was to develop quantitative measures for the assessment of laryngeal function using speech and electroglottographic (EGG) data. We developed two procedures for the detection of laryngeal pathology: 1) a spectral distortion measure using pitch synchronous and asynchronous methods with linear predictive coding (LPC) vectors and vector quantization (VQ) and 2) analysis of the EGG signal using time interval and amplitude difference measures. The VQ procedure was conjectured to offer the possibility of circumventing the need to estimate the glottal volume velocity wave-form by inverse filtering techniques. The EGG procedure was to evaluate data that was "nearly" a direct measure of vocal fold vibratory motion and thus was conjectured to offer the potential for providing an excellent assessment of laryngeal function. A threshold based procedure gave 75.9 and 69.0% probability of pathological detection using procedures 1) and 2), respectively, for 29 patients with pathological voices and 52 normal subjects. The false alarm probability was 9.6% for the normal subjects.

FAST TRACK COMMUNICATION: Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd k

NASA Astrophysics Data System (ADS)

Quesne, C.

2010-02-01

In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k >= 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian {\\cal H}_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion {\\cal Y}_{2k}, from which Y2k can be obtained by projection in the D2k identity representation space.

Algebraic cycles and local anomalies in F-theory

NASA Astrophysics Data System (ADS)

Bies, Martin; Mayrhofer, Christoph; Weigand, Timo

2017-11-01

We introduce a set of identities in the cohomology ring of elliptic fibrations which are equivalent to the cancellation of gauge and mixed gauge-gravitational anomalies in F-theory compactifications to four and six dimensions. The identities consist in (co)homological relations between complex codimension-two cycles. The same set of relations, once evaluated on elliptic Calabi-Yau three-folds and four-folds, is shown to universally govern the structure of anomalies and their Green-Schwarz cancellation in six- and four-dimensional F-theory vacua, respectively. We furthermore conjecture that these relations hold not only within the cohomology ring, but even at the level of the Chow ring, i.e. as relations among codimension-two cycles modulo rational equivalence. We verify this conjecture in non-trivial examples with Abelian and non-Abelian gauge groups factors. Apart from governing the structure of local anomalies, the identities in the Chow ring relate different types of gauge backgrounds on elliptically fibred Calabi-Yau four-folds.

The SU(r)2 string functions as q-diagrams

NASA Astrophysics Data System (ADS)

Genish, Arel; Gepner, Doron

2016-06-01

A generalized Roger Ramanujan (GRR) type expression for the characters of A-type parafermions has been a long standing puzzle dating back to conjectures made regarding some of the characters in the 90s. Not long ago we have put forward such GRR type identities describing any of the level two ADE-type generalized parafermions characters at any rank. These characters are the string functions of simply laced Lie algebras at level two, as such, they are also of mathematical interest. In our last joint paper we presented the complete derivation for the D-type generalized parafermions characters identities. Here we generalize our previous discussion and prove the GRR type expressions for the characters of A-type generalized parafermions. To prove the A-type GRR conjecture we study further the q-diagrams, introduced in our last joint paper, and examine the diagrammatic interpretations of known identities among them Slater identities for the characters of the first minimal model, which is the Ising model, and the Bailey lemma.

An ill-posed problem for the Black-Scholes equation for a profitable forecast of prices of stock options on real market data

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Kuzhuget, Andrey V.; Golubnichiy, Kirill V.

2016-01-01

A new empirical mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock, new initial and new boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. To verify the validity of our model, real market data for 368 randomly selected liquid options are used. A new trading strategy is proposed. Our results indicates that our method is profitable on those options. Furthermore, it is shown that the performance of two simple extrapolation-based techniques is much worse. We conjecture that our method might lead to significant profits of those financial insitutions which trade large amounts of options. We caution, however, that further studies are necessary to verify this conjecture.

On a three-dimensional symmetric Ising tetrahedron and contributions to the theory of the dilogarithm and Clausen functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coffey, Mark W.

2008-04-15

Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron C{sup Tet}{identical_to}C(1,1) has been of interest from many points of view, with several representations and conjectures having been given in the literature. We prove a conjectured exponentially fast convergent sum for C(1,1), as well as a previously empirical relation for C(1,1) as a remarkable difference of Clausen function values. Our presentation includes propositions extending the theory of the dilogarithm Li{sub 2} and Clausen Cl{sub 2} functions,more » as well as their relation to other special functions of mathematical physics. The results strengthen connections between Feynman diagram integrals, volumes in hyperbolic space, number theory, and special functions and numbers, specifically including dilogarithms, Clausen function values, and harmonic numbers.« less

A Probabilistic Model of Local Sequence Alignment That Simplifies Statistical Significance Estimation

PubMed Central

Eddy, Sean R.

2008-01-01

Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (λ) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty (“Forward” scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores (“Viterbi” scores) are Gumbel-distributed with constant λ = log 2, and the high scoring tail of Forward scores is exponential with the same constant λ. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments. PMID:18516236

How do rituals affect cooperation? An experimental field study comparing nine ritual types.

PubMed

Fischer, Ronald; Callander, Rohan; Reddish, Paul; Bulbulia, Joseph

2013-06-01

Collective rituals have long puzzled anthropologists, yet little is known about how rituals affect participants. Our study investigated the effects of nine naturally occurring rituals on prosociality. We operationalized prosociality as (1) attitudes about fellow ritual participants and (2) decisions in a public goods game. The nine rituals varied in levels of synchrony and levels of sacred attribution. We found that rituals with synchronous body movements were more likely to enhance prosocial attitudes. We also found that rituals judged to be sacred were associated with the largest contributions in the public goods game. Path analysis favored a model in which sacred values mediate the effects of synchronous movements on prosocial behaviors. Our analysis offers the first quantitative evidence for the long-standing anthropological conjecture that rituals orchestrate body motions and sacred values to support prosociality. Our analysis, moreover, adds precision to this old conjecture with evidence of a specific mechanism: ritual synchrony increases perceptions of oneness with others, which increases sacred values to intensify prosocial behaviors.

Quasinormal Modes and Strong Cosmic Censorship.

PubMed

Cardoso, Vitor; Costa, João L; Destounis, Kyriakos; Hintz, Peter; Jansen, Aron

2018-01-19

The fate of Cauchy horizons, such as those found inside charged black holes, is intrinsically connected to the decay of small perturbations exterior to the event horizon. As such, the validity of the strong cosmic censorship (SCC) conjecture is tied to how effectively the exterior damps fluctuations. Here, we study massless scalar fields in the exterior of Reissner-Nordström-de Sitter black holes. Their decay rates are governed by quasinormal modes of the black hole. We identify three families of modes in these spacetimes: one directly linked to the photon sphere, well described by standard WKB-type tools; another family whose existence and time scale is closely related to the de Sitter horizon; finally, a third family which dominates for near-extremally charged black holes and which is also present in asymptotically flat spacetimes. The last two families of modes seem to have gone unnoticed in the literature. We give a detailed description of linear scalar perturbations of such black holes, and conjecture that SCC is violated in the near extremal regime.

Quasinormal Modes and Strong Cosmic Censorship

NASA Astrophysics Data System (ADS)

Cardoso, Vitor; Costa, João L.; Destounis, Kyriakos; Hintz, Peter; Jansen, Aron

2018-01-01

The fate of Cauchy horizons, such as those found inside charged black holes, is intrinsically connected to the decay of small perturbations exterior to the event horizon. As such, the validity of the strong cosmic censorship (SCC) conjecture is tied to how effectively the exterior damps fluctuations. Here, we study massless scalar fields in the exterior of Reissner-Nordström-de Sitter black holes. Their decay rates are governed by quasinormal modes of the black hole. We identify three families of modes in these spacetimes: one directly linked to the photon sphere, well described by standard WKB-type tools; another family whose existence and time scale is closely related to the de Sitter horizon; finally, a third family which dominates for near-extremally charged black holes and which is also present in asymptotically flat spacetimes. The last two families of modes seem to have gone unnoticed in the literature. We give a detailed description of linear scalar perturbations of such black holes, and conjecture that SCC is violated in the near extremal regime.

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Jaewon

We present superconformal indices of 4d N = 2 class S theories with certain irregular punctures called type I k,N. This class of theories include generalized Argyres-Douglas theories of type (A k-1, A N-1) and more. We conjecture the superconformal indices in certain simplifi ed limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture I k,N. We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index andmore » the Macdonald index for odd N. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the (A 1,A 2n) theory. In addition, we discuss the mixed Schur indices for the N = 1 class S theories with irregular punctures.« less