Subsets of configurations and canonical partition functions
Bloch, J.; Bruckmann, F.; Kieburg, M.;
2013-01-01
We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: the subset sum over configurations is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition f...... function is independent of the chemical potential, the zero-quark-charge sector provides the full result. © 2013 American Physical Society....
Narasimhan, S L; Krishna, P S R; Ponmurugan, M; Murthy, K P N
2008-01-01
We have explained in detail why the canonical partition function of interacting self-avoiding walk (ISAW) is exactly equivalent to the configurational average of the weights associated with growth walks, such as the interacting growth walk (IGW), if the average is taken over the entire genealogical tree of the walk. In this context, we have shown that it is not always possible to factor the density of states out of the canonical partition function if the local growth rule is temperature dependent. We have presented Monte Carlo results for IGWs on a diamond lattice in order to demonstrate that the actual set of IGW configurations available for study is temperature dependent even though the weighted averages lead to the expected thermodynamic behavior of ISAW. PMID:18190183
A simple way of approximating the canonical partition functions in statistical mechanics
Fernández, Francisco M.
2015-09-01
We propose a simple pedagogical way of introducing the Euler-MacLaurin summation formula in an undergraduate course on statistical mechanics. The reason is that the students may feel more comfortable and confident if they are able to deduce the main equations. To this end we put forward two alternative routes: the first one is the simplest and yields the first two terms of the expansion. The second one is somewhat more elaborate and takes into account all the correction terms. We apply both to the calculation of the simplest one-particle canonical partition functions for the translational, vibrational and rotational degrees of freedom. The more elaborate, systematic calculation of the correction terms is suitable for motivating the students to explore the possibility of using available computer algebra software that enable one to avoid long and tedious manipulation of algebraic equations.
Lee, S. J.; Mekjian, A. Z.
2004-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a, x, z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a,x,z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given
Brambilla, M; Ugoccioni, R
2006-01-01
Theorems on zeros of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeros of the grand canonical partition function which allow us to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.
Brambilla, M.; Giovannini, A.; Ugoccioni, R.
2006-06-01
Theorems on zeros of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeros of the grand canonical partition function which allow us to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.
Brambilla, M.; Giovannini, A.; Ugoccioni, R.
2005-01-01
Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeroes of the grand canonical partition function which allow to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.
Lee, S J
2002-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent emission or Poisson processes, chaotic emission resulting in a negative binomial distribution, combinations of coherent and chaotic processes called signal/noise distributions, and models based on field emission from Lorentzian line shapes leading to Lorentz/Catalan distributions. These specific cases can be written as special cases of a more general distribution. Using this grand canonical approach moments and cumulants, combinants, hierarchical structure, void scaling relations, KNO scaling features, clan variables and branching laws associated with stochastic or ancestral variables are discussed. It is shown that just looking at the mean and fluctuation of data is not enough to distinguish these distributions or the underlying mechanism. A generalization of the Poisson tran...
Hryniv, R O
2001-01-01
We study the self-avoiding polygons (SAP) connecting the vertical and the horizontal semi-axes of the positive quadrant of $\\mathbb{Z}^2$. For a fixed $\\beta>0$, assign to each such polygon $\\omega$ the weight $\\exp\\{-\\beta|\\omega|\\}$, $|\\omega|$ denoting the length of $\\omega$, and consider the sum $Z_{Q,+}$ of these weights for all SAP enclosing area $Q>0$. We study the statistical properties of such SAP and, in particular, derive the exact asymptotics for the partition function $Z_{Q,+}$ as $Q\\to\\infty$. The results are valid for any $\\beta >\\beta_c$, $\\beta_c$ being the critical value for the 2D self-avoiding walks.
Lee, S. J.; Mekjian, A. Z.
2003-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ wit...
Lee, S J
2004-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ with Fisher's critical exponent $\\tau$ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent $\\tau$. Various physical phenomena such as hierarchical structure, void scaling relations, KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative bino...
Rocha, Julio; Mol, Lucas; Costa, Bismarck
2015-03-01
In this work we show that the canonical partition function zeros, the Fisher zeros, can be used to uniquely characterize a transition as being in the Berezinskii-Kosterlitz-Thouless (BKT) class of universality. By studying the zeros map for the 2D XY model we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the BKT transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the BKT class of universality from other ones. This work was partially supported by CNPq and Fapemig, Brazilian Agencies.
Kellerstein, M; Verbaarschot, J J M
2016-01-01
The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wagner theorem. One possible resolution of this paradox is that, because of the bosonic determinant in the partially quenched partition function, the conditions of this theorem are violated allowing for spontaneous symmetry breaking in two dimensions or less. This goes back to work by Niedermaier and Seiler on nonamenable symmetries of the hyperbolic spin chain and earlier work by two of the auhtors on bosonic partition functions at nonzero chemical potential. In this talk we discuss chiral symmetry breaking for the bosonic partition function of QCD at nonzero isospin chemical potential and a bosonic random matrix theory at imaginary chemical potential and compare the results with the fermionic counterpart. In both cases the chiral symmetry group of the bosonic partition function is noncompact.
Functional Multiple-Set Canonical Correlation Analysis
Hwang, Heungsun; Jung, Kwanghee; Takane, Yoshio; Woodward, Todd S.
2012-01-01
We propose functional multiple-set canonical correlation analysis for exploring associations among multiple sets of functions. The proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered. As in classical multiple-set canonical correlation analysis, computationally, the…
Partition density functional theory
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
Matrix string partition function
Kostov, Ivan K; Kostov, Ivan K.; Vanhove, Pierre
1998-01-01
We evaluate quasiclassically the Ramond partition function of Euclidean D=10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasiclassical calculation might be exact.
Generalised twisted partition functions
Petkova, V B
2001-01-01
We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.
Functional linear regression via canonical analysis
He, Guozhong; Wang, Jane-Ling; Yang, Wenjing; 10.3150/09-BEJ228
2011-01-01
We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of functional linear regression analysis. A specific procedure for the estimation of the regression parameter function using canonical expansions is proposed and compared with an established functional principal component regression approach. As an example of an application, we present an analysis of mortality data for cohorts of medflies, obtained in experimental studies of aging and longevity.
Canonic form of linear quaternion functions
Sangwine, Stephen J.
2008-01-01
The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown that any such function may be represented using at most four quaternion coefficients. In this paper, a new and simple method is presented for obtaining these coefficients numerically using a matrix approach which also gives an alternative proof of the canonic ...
Partial domain wall partition functions
Foda, O.; Wheeler, M.
2012-01-01
We consider six-vertex model configurations on an n-by-N lattice, n =< N, that satisfy a variation on domain wall boundary conditions that we define and call "partial domain wall boundary conditions". We obtain two expressions for the corresponding "partial domain wall partition function", as an (N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions...
On higher spin partition functions
Beccaria, M
2015-01-01
We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the "physical" ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z=1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z=1 is also true in the conformal higher spin theory (with higher-derivative d^{2s} kinetic terms) expanded near flat or conformally flat S^4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat space. This non...
On higher spin partition functions
Beccaria, Matteo; Tseytlin, Arkady A.
2015-07-01
We observe that the partition function of the set of all free massless higher spins s = 0, 1, 2, 3,... in flat space is equal to one: the ghost determinants cancel against the ‘physical’ ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z = 1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z = 1 is true also in the conformal higher spin theory (with higher-derivative {\\partial }2s kinetic terms) expanded near flat or conformally flat S4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat 4d space. This non-unitary theory has Weyl-invariant action in curved background and it corresponds to ‘partially massless’ field in AdS5. We discuss in detail the special case of s = 2 (or ‘conformal graviton’), compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions.
The Functional Determinant and the Partition Function in Geometric Flows
Lin, Christopher
2013-01-01
We propose the use of the functional determinant of geometric operators in constructing an entropy functional associated to geometric flows. Our approach is based on the direct computation of the partition function, with a well-defined set of microstates and macrostates in the canonical ensemble. The approach is motivated by a fundamental enigma in Perelman's derivation of his famous $\\mathcal{W}$-entropy. The defining feature of our entropy is that the energy of each microstate in the partition function is invariant along the associated geometric flow - a clue that could be inferred from Perelman's work. Moreover, the monotonicity of our entropy along the associated geometric flow is then a natural result in the statistical mechanics framework. While we will not argue in a completely rigorous manner, we will use the formalism to derive an explicit formula for an entropy associated to conformal flows on a closed surface based on the Polyakov formula for the determinant of the Laplacian. We also discuss possib...
Approximate path integral methods for partition functions
We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising method is one based upon an approximation to the path integral expression of the partition function. In this method, the partition-function expression has the ease of evaluation of a classical partition function, and quantum mechanical effects are included by a weight function. Anharmonicity is included exactly in the classical Boltzmann average and local quadratic expansions around the centroid of the quantum paths yield a simple analytic form for the quantum weight function. We discuss the relationship between this expression and previous approximate methods and present numerical comparisons for model one-dimensional potentials and for accurate three-dimensional vibrational force fields for H2O and SO2
Desgranges, Caroline; Delhommelle, Jerome
2016-03-28
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si. PMID:27036464
Desgranges, Caroline; Delhommelle, Jerome
2016-03-01
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.
Partial domain wall partition functions
Foda, O
2012-01-01
We consider six-vertex model configurations on a rectangular lattice with n (N) horizontal (vertical) lines, and "partial domain wall boundary conditions" defined as 1. all 2n arrows on the left and right boundaries point inwards, 2. n_u (n_l) arrows on the upper (lower) boundary, such that n_u + n_l = N - n, also point inwards, 3. all remaining n+N arrows on the upper and lower boundaries point outwards, and 4. all spin configurations on the upper and lower boundaries are summed over. To generate (n-by-N) "partial domain wall configurations", one can start from A. (N-by-N) configurations with domain wall boundary conditions and delete n_u (n_l) upper (lower) horizontal lines, or B. (2n-by-N) configurations that represent the scalar product of an n-magnon Bethe eigenstate and an n-magnon generic state on an N-site spin-1/2 chain, and delete the n lines that represent the Bethe eigenstate. The corresponding "partial domain wall partition function" is computed in construction {A} ({B}) as an N-by-N (n-by-n) det...
Canonical Duality Theory for Solving Minimization Problem of Rosenbrock Function
Gao, David Y.; Zhang, Jiapu
2011-01-01
This paper presents a canonical duality theory for solving nonconvex minimization problem of Rosenbrock function. Extensive numerical results show that this benchmark test problem can be solved precisely and efficiently to obtain global optimal solutions.
Perturbative partition function for squashed S^5
Imamura, Yosuke
2012-01-01
We compute the index of 6d N=(1,0) theories on S^5xR containing vector and hypermultiplets. We only consider the perturbative sector without instantons. By compactifying R to S^1 with a twisted boundary condition and taking the small radius limit, we derive the perturbative partition function on a squashed S^5. The 1-loop partition function is represented in a simple form with the triple sine function.
Grand partition function of hadronic bremsstrahlung
The grand partition function of hadronic bremsstrahlung is obtained using saddle-point procedures. Several levels of approximation are considered. The results are qualitatively consistent with earlier simple approximations
Statistical thermodynamics in relativistic particle and ion physics: Canonical or grand canonical
We consider relativistic statistical thermodynamics of an ideal Boltzmann gas consisting of the particles K, Λ, A, Σ and their antiparticles. Baryon number (B) and strangeness (S) are conserved. While any relativistic gas is necessarily grand canonical with respect to particle numbers, conservation laws can be treated canonically or grand canonically. We construct the partition function for canonical BxS conservation and compare it with the grand canonical one. It is found that the grand canonical partition function is equivalent to a large B approximation of the canonical one. The relative difference between canonical and grand canonical quantities seems to decrease like const/B (two numerical examples) and from this a simple thumb rule for computing canonical quantities from grand canonical ones is guessed. For precise calculations, an integral representation is given. (orig.)
Partition Function of Interacting Calorons Ensemble
Deldar, Sedigheh
2015-01-01
We present a method for computing the partition function of a caloron ensemble taking into account the interaction of calorons. We focus on caloron-Dirac string interaction and show that the metric that Diakonov and Petrov offered works well in the limit where this interaction occurs. We suggest computing the correlation function of two polyakov loops by applying Ewald's method.
Partition function of interacting calorons ensemble
Deldar, S.; Kiamari, M.
2016-01-01
We present a method for computing the partition function of a caloron ensemble taking into account the interaction of calorons. We focus on caloron-Dirac string interaction and show that the metric that Diakonov and Petrov offered, works well in the limit where this interaction occurs. We suggest computing the correlation function of two polyakov loops by applying Ewald's method.
Domain wall partition functions and KP
We observe that the partition function of the six-vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP τ function and express it as an expectation value of charged free fermions (up to an overall normalization)
Domain wall partition functions and KP
Foda, O; Zuparic, M
2009-01-01
We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).
Partition functions and graphs: A combinatorial approach
Solomon, A I; Duchamp, G; Horzela, A; Penson, K A; Solomon, Allan I.; Blasiak, Pawel; Duchamp, Gerard; Horzela, Andrzej; Penson, Karol A.
2004-01-01
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman-type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a superfluid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequen...
Twist-4 effects in electroproduction: Canonical operators and coefficient functions
The interpretation of observed scaling violations in leptoproduction is complicated by the possible presence of significant higher-twist effects. We refine the machinery of the operator-product expansion sufficiently for a study of twist-4 effects. In particular, we introduce and review the advantages of a special, ''canonical'' basis. We demonstrate that the canonical basis is adequate for the necessary twist-4 perturbative calculations, and calculate the operator's tree-level coefficient functions in electroproduction. Our results establish a framework within which careful analysis of more accurate data can provide information regarding correlations among the constituents of the proton
Derivation of Mayer Series from Canonical Ensemble
Xian-Zhi, Wang
2016-02-01
Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.
Indefinite theta functions and black hole partition functions
We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions
Indefinite theta functions and black hole partition functions
Cardoso, Gabriel Lopes; Cirafici, Michele [Center for Mathematical Analysis, Geometry, and Dynamical Systems,Departamento de Matemática and LARSyS, Instituto Superior Técnico,1049-001 Lisboa (Portugal); Jorge, Rogério [Instituto Superior Técnico,1049-001 Lisboa (Portugal); Nampuri, Suresh [Laboratoire de Physique Théorique, École Normale Supérieure,24 rue Lhomond, 75231 Paris Cedex 05 (France)
2014-02-05
We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions.
Virasoro constraint for Nekrasov instanton partition function
Kanno, Shoichi; Zhang, Hong
2012-01-01
We show that Nekrasov instanton partition function for SU(N) gauge theories satisfies recursion relations in the form of U(1)+Virasoro constraints when {\\beta} = 1. The constraints give a direct support for AGT conjecture for general quiver gauge theories.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2016-02-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2015-01-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)
2016-02-15
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
Some reference formulas for the generating functions of canonical transformations
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
A canonical correlation analysis of intelligence and executive functioning.
Davis, Andrew S; Pierson, Eric E; Finch, W Holmes
2011-01-01
Executive functioning is one of the most researched and debated topics in neuropsychology. Although neuropsychologists routinely consider executive functioning and intelligence in their assessment process, more information is needed regarding the relationship between these constructs. This study reports the results of a canonical correlation study between the most widely used measure of adult intelligence, the Wechsler Adult Intelligence Scale, 3rd edition (WAIS-III; Wechsler, 1997), and the Delis-Kaplan Executive Function System (D-KEFS; Delis, Kaplan, & Kramer, 2001). The results suggest that, despite considerable shared variability, the measures of executive functioning maintain unique variance that is not encapsulated in the construct of global intelligence. PMID:21390902
Sifting Function Partition for the Goldbach Problem
Song, Fu-Gao
2008-01-01
All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so and which is, in general, very difficult. Some new methods introduced in this paper show that the Goldbach problem can be solved under sifting out only some composite numbers. In fact, in order to prove the Goldbach conjecture, it is only necessary to show that there are prime numbers left in the residual integers after the initial sifting! This idea can be implemented by using one of the three methods called sifting function partition by integer sort, sifting function partition by intervals and comparative sieve method, respectively. These are feasible methods for solving both the Goldbach problem and the problem of twin primes. An added bonus of the above methods is the elimination of the indeterminacy of the sifting functions brought about by their upper and lower bounds.
Supersymmetric partition functions on Riemann surfaces
Benini, Francesco
2016-01-01
We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on $\\Sigma_g \\times T^n$ with partial topological twist on $\\Sigma_g$, where $\\Sigma_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$. For genus g=1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on $\\Sigma_g \\times S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS4 whose horizon has $\\Sigma_g$ topology.
On partition function in Astronomy \\& Astrophysics
Sharma, M K; Chandra, Suresh
2015-01-01
In order to analyze spectrum from the interstellar medium (ISM), spectrum of the molecule of interest is recorded in a laboratory, and accurate rotational and centrifugal distortion constants are derived. By using these constants, one can calculate accurate partition function. However, in the same paper, where these constants are derived, the partition function is calculated by using a semi-empirical expression. We have looked into the details of this semi-empirical expression and compared the values, obtained from it, with the accurate ones. As an example, we have considered the case of Methanimine (CH$_2$NH) which is detected in a number of cosmic objects. It is found that for the kinetic temperature $T > 120$ K, the semi-empirical expression gives large value as compared to the accurate one. The deviation becomes about 25\\% larger than the accurate one at the kinetic temperature of 400 K.
The geometry of supersymmetric partition functions
Cyril Closset; Dumitrescu, Thomas T.; Guido Festuccia; Zohar Komargodski
2014-01-01
We consider supersymmetric field theories on compact manifolds $ \\mathcal{M} $ and obtain constraints on the parameter dependence of their partition functions $ {Z_{\\mathcal{M}}} $ . Our primary focus is the dependence of $ {Z_{\\mathcal{M}}} $ on the geometry of $ \\mathcal{M} $ , as well as background gauge fields that couple to continuous flavor symmetries. For $ \\mathcal{N} $ = 1 theories with a U(1) R symmetry in four dimensions, $ \\mathcal{M} $ must be a complex manifold with a Hermitian ...
Superfluid Kubo Formulas from Partition Function
Chapman, Shira; Oz, Yaron
2014-01-01
Linear response theory relates hydrodynamic transport coefficients to equilibrium retarded correlation functions of the stress-energy tensor and global symmetry currents in terms of Kubo formulas. Some of these transport coefficients are non-dissipative and affect the fluid dynamics at equilibrium. We present an algebraic framework for deriving Kubo formulas for such thermal transport coefficients by using the equilibrium partition function. We use the framework to derive Kubo formulas for all such transport coefficients of superfluids, as well as to rederive Kubo formulas for various normal fluid systems.
Denominator function for canonical SU(3) tensor operators
The definition of a canonical unit SU(3) tensor operator is given in terms of its characteristic null space as determined by group-theoretic properties of the intertwining number. This definition is shown to imply the canonical splitting conditions used in earlier work for the explicit and unique (up to +- phases) construction of all SU(3) WCG coefficients (Wigner--Clebsch--Gordan). Using this construction, an explicit SU(3)-invariant denominator function characterizing completely the canonically defined WCG coefficients is obtained. It is shown that this denominator function (squared) is a product of linear factors which may be obtained explicitly from the characteristic null space times a ratio of polynomials. These polynomials, denoted G/sup t//sub q/, are defined over three (shift) parameters and three barycentric coordinates. The properties of these polynomials (hence, of the corresponding invariant denominator function) are developed in detail: These include a derivation of their degree, symmetries, and zeros. The symmetries are those induced on the shift parameters and barycentric coordinates by the transformations of a 3 x 3 array under row interchange, column interchange, and transposition (the group of 72 operations leaving a 3 x 3 determinant invariant). Remarkably, the zeros of the general G/sup t//sub q/ polynomial are in position and multiplicity exactly those of the SU(3) weight space associated with irreducible representation [q-1,t-1,0]. The results obtained are an essential step in the derivation of a fully explicit and comprehensible algebraic expression for all SU(3) WCG coefficients
Surface defects and instanton partition functions
Gaiotto, Davide
2014-01-01
We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is valid for defects which can be given a "vortex construction", i.e. can be defined by RG flow from vortex configurations in a larger theory. We test the prescription against known results and expected dualities. We employ our prescription to develop a general computational strategy for defects defined by coupling the bulk degrees of freedom to a Gauged Linear Sigma Model living in co-dimension two.
Partition functions, duality and the tube metric
The partition function of type IIA and B strings on R6 x K3, in the T4/Z2 orbifold limit, is explicitly computed as a modular invariant sum over spin structures required by perturbative unitarity in order to extend the analysis to include type II strings on R6 x W4, where W4 is associated with the tube metric conformal field theory, given by the degrees of freedom transverse to the Neveu-Schwarz fivebrane solution. This generates partition functions and perturbative spectra of string theories in six space-time dimensions, associated with the modular invariants of the level-k affine SU(2) Kac-Moody algebra. These theories provide a conformal field theory (i.e. perturbative) probe of non-perturbative (fivebrane) vacua. We contrast them with theories whose N=(4,4) sigma-model action contains nH=k+2 hypermultiplets as well as vector supermultiplets, and where k is the level just mentioned. In Appendix B we also give a D=6, N=(1,1) 'free fermion' string model which has a different moduli space of vacua from the 81-parameter space relevant to the above examples. (orig.)
Partition function for a singular background
We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the local Born approximation (LBA)
Modular properties of full 5D SYM partition function
Qiu, Jian; Tizzano, Luigi; Winding, Jacob; Zabzine, Maxim
2016-03-01
We study properties of the full partition function for the U(1) 5D N = {2}^{ast } gauge theory with adjoint hypermultiplet of mass M . This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function G 2 C associated with a certain moment map cone C. The answer exhibits a curious SL(4 , ℤ) modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5d supersymmetric partition function with the insert ion of defects of various co-dimensions.
S^3/Z_n partition function and dualities
Imamura, Yosuke
2012-01-01
We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle points with different holonomies. An appropriate choice of the phase of each contribution is essential to obtain the partition function. We determine the relative phases in the holonomy sum in a few examples by using duality to non-gauge theories. In the case of odd n the phase factors can be absorbed by modifying a single function appearing in the partition function.
Partition function of nearest neighbour Ising models: Some new insights
G Nandhini; M V Sangaranarayanan
2009-09-01
The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic 2 × 2 matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed.
Frady, E Paxon; Kapoor, Ashish; Horvitz, Eric; Kristan, William B
2016-08-01
Large-scale data collection efforts to map the brain are underway at multiple spatial and temporal scales, but all face fundamental problems posed by high-dimensional data and intersubject variability. Even seemingly simple problems, such as identifying a neuron/brain region across animals/subjects, become exponentially more difficult in high dimensions, such as recognizing dozens of neurons/brain regions simultaneously. We present a framework and tools for functional neurocartography-the large-scale mapping of neural activity during behavioral states. Using a voltage-sensitive dye (VSD), we imaged the multifunctional responses of hundreds of leech neurons during several behaviors to identify and functionally map homologous neurons. We extracted simple features from each of these behaviors and combined them with anatomical features to create a rich medium-dimensional feature space. This enabled us to use machine learning techniques and visualizations to characterize and account for intersubject variability, piece together a canonical atlas of neural activity, and identify two behavioral networks. We identified 39 neurons (18 pairs, 3 unpaired) as part of a canonical swim network and 17 neurons (8 pairs, 1 unpaired) involved in a partially overlapping preparatory network. All neurons in the preparatory network rapidly depolarized at the onsets of each behavior, suggesting that it is part of a dedicated rapid-response network. This network is likely mediated by the S cell, and we referenced VSD recordings to an activity atlas to identify multiple cells of interest simultaneously in real time for further experiments. We targeted and electrophysiologically verified several neurons in the swim network and further showed that the S cell is presynaptic to multiple neurons in the preparatory network. This study illustrates the basic framework to map neural activity in high dimensions with large-scale recordings and how to extract the rich information necessary to perform
On the canonical decomposition of generalized modular functions
Kohnen, Winfried
2010-01-01
The authors have conjectured (\\cite{KoM}) that if a normalized generalized modular function (GMF) $f$, defined on a congruence subgroup $\\Gamma$, has integral Fourier coefficients, then $f$ is classical in the sense that some power $f^m$ is a modular function on $\\Gamma$. A strengthened form of this conjecture was proved (loc cit) in case the divisor of $f$ is \\emph{empty}. In the present paper we study the canonical decomposition of a normalized parabolic GMF $f = f_1f_0$ into a product of normalized parabolic GMFs $f_1, f_0$ such that $f_1$ has \\emph{unitary character} and $f_0$ has \\emph{empty divisor}. We show that the strengthened form of the conjecture holds if the first "few" Fourier coefficients of $f_1$ are algebraic. We deduce proofs of several new cases of the conjecture, in particular if either $f_0=1$ or if the divisor of $f$ is concentrated at the cusps of $\\Gamma$.
Superconformal indices and partition functions for supersymmetric field theories
Gahramanov, I.B. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.
N=4 superconformal characters and partition functions
Character formulae for positive energy unitary representations of the N=4 superconformal group are obtained through use of reduced Verma modules and Weyl group symmetry. Expansions of these are given which determine the particular representations present and results such as dimensions of superconformal multiplets. By restriction of variables various 'blind' characters are also obtained. Limits, corresponding to reduction to particular subgroups, in the characters isolate contributions from particular subsets of multiplets and in many cases simplify the results considerably. As a special case, the index counting short and semi-short multiplets which do not form long multiplets found recently is shown to be related to particular cases of reduced characters. Partition functions of N=4 super-Yang-Mills are investigated. Through analysis of these, exact formulae are obtained for counting 12- and some 14-BPS operators in the free case. Similarly, partial results for the counting of semi-short operators are given. It is also shown in particular examples how certain short operators which one might combine to form long multiplets due to group theoretic considerations may be protected dynamically
Partition Function of the Ising Model via Factor Graph Duality
Molkaraie, Mehdi
2013-01-01
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition function of the Ising model. In the one-dimensional case, we thus obtain an alternative derivation of the (well-known) analytical solution. In the two-dimensional case, we find that Monte Carlo methods are much more efficient on the dual graph than on the original graph, especially at low temperature.
Graph theory and Pfaffian representations of Ising partition function
Gobron, Thierry
2013-01-01
48 pages A well known theorem due to Kasteleyn states that the partition function of an Ising model on an arbitrary planar graph can be represented as the Pfaffian of a skew-symmetric matrix associated to the graph. This results both embodies the free fermionic nature of any planar Ising model and eventually gives an effective way of computing its partition functions in closed form. An extension of this result to non planar models expresses the partition function as a sum of Pfaffians whic...
String partition functions in Rindler space and maximal acceleration
Mertens, Thomas G; Zakharov, Valentin I
2015-01-01
We revisit non-interacting string partition functions in Rindler space by summing over fields in the spectrum. Using recent results of JHEP 1505 (2015) 106, this construction, first done by Emparan, can be put on much firmer ground. For open strings, we demonstrate that surface contributions to the higher spin fields correspond to open strings piercing the Rindler origin, unifying the higher spin surface contributions in string language. We generalize the construction of these partition functions to type II and heterotic superstrings and demonstrate modular invariance for the resulting partition functions. Also, explicit signs of spacetime supersymmetry are visible. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration with $T_{\\text{crit}} = T_{H}/\\pi$ close to the black hole horizon. Ultimately, these partition functions are not physical, and divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the h...
The M2/M5 BPS Partition Functions from Supergravity
Silva, Pedro J
2009-01-01
In the framework of the AdS/CFT duality, we calculate the supersymmetric partition function of the superconformal field theories living in the world volume of either $N$ $M2$-branes or $N$ $M5$-branes. We used the dual supergravity partition function in a saddle point approximation over supersymmetric Black Holes. Since our BHs are written in asymptotically global $AdS_{d+1}$ co-ordinates, the dual SCFTs are in $R x S^{d}$ for $d=2,5$. The resulting partition function shows phase transitions, constraints on the phase space and allowed us to identify unstable BPS Black hole in the $AdS$ phase. This configurations should corresponds to unstable configurations in the dual theory. We also report an intriguing relation between the most general Witten Index, computed in the above theories, and our BPS partition functions.
Factorization of S^3/Z_n partition function
Imamura, Yosuke; Yokoyama, Daisuke
2013-01-01
We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative signs among the contributions. We argue that the factorization to holomorphic blocks is a useful criterion to determine the signs and propose a formula for them. We show that the orbifold partition function of a general non-gauge theory is correctly factorized provided that we take appropriate relative signs. We also present a few examples of gauge theories. We point out that the sign factor for the orbifold partition function is closely related to a similar sign factor in the lens space index and the 3d index.
On the parity of generalized partition functions, III.
Ben Said, Fethi; Nicolas, Jean-Louis; Zekraoui, Ahlem
2010-01-01
International audience Improving on some results of J.-L. Nicolas, the elements of the set ${\\cal A}={\\cal A}(1+z+z^3+z^4+z^5)$, for which the partition function $p({\\cal A},n)$ (i.e. the number of partitions of $n$ with parts in ${\\cal A}$) is even for all $n\\geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.
Partition function of the trigonometric SOS model with reflecting end
Filali, Ghali
2010-01-01
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Line defects and 5d instanton partition functions
Kim, Hee-Cheol
2016-03-01
We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter x, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N . Nekrasov is briefly discussed.
Line defects and 5d instanton partition functions
Kim, Hee-Cheol
2016-01-01
We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter $x$, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N. Nekrasov is briefly discussed.
A brief history of partitions of numbers, partition functions and their modern applications
Debnath, Lokenath
2016-04-01
'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.
Partition function of massless scalar field in Schwarzschild background
Sanyal, Abhik Kumar
2014-01-01
Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.
Canonical and alternate functions of the microRNA biogenesis machinery
Chong, Mark M.W.; Zhang, Guoan; Cheloufi, Sihem; Neubert, Thomas A.; Hannon, Gregory J.; Littman, Dan R.
2010-01-01
The canonical microRNA (miRNA) biogenesis pathway requires two RNaseIII enzymes: Drosha and Dicer. To understand their functions in mammals in vivo, we engineered mice with germline or tissue-specific inactivation of the genes encoding these two proteins. Changes in proteomic and transcriptional profiles that were shared in Dicer- and Drosha-deficient mice confirmed the requirement for both enzymes in canonical miRNA biogenesis. However, deficiency in Drosha or Dicer did not always result in ...
Graphs of partitions and Ramanujan's tau-function
Brent, Barry
2004-01-01
The invariant z_{lambda} attached to a partition lambda sits in the denominator of the Girard-Waring solution to Newton's symmetric function relations. We interpret Ramanujan's tau-function in terms of z_lambda, and interpret z_lambda in terms of the automorphisms of a graph.
Constraints on Fluid Dynamics from Equilibrium Partition Functions
Banerjee, Nabamita; Bhattacharyya, Sayantani; Jain, Sachin; Minwalla, Shiraz; Sharma, Tarun
2012-01-01
We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with ...
Approximation methods for the partition functions of anharmonic systems
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations
Revisiting noninteracting string partition functions in Rindler space
Mertens, Thomas G.; Verschelde, Henri; Zakharov, Valentin I.
2016-05-01
We revisit noninteracting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way into a piece that does not contain surface terms and a piece consisting of solely the so-called edge states. For open strings, we illustrate that surface contributions to the higher-spin fields correspond to open strings piercing the Rindler origin, unifying the higher-spin surface contributions in string language. For closed strings, we demonstrate that the string partition function is not quite the same as the sum over the partition functions of the fields in the spectrum: an infinite overcounting is present for the latter. Next we study the partition functions obtained by excluding the surface terms. Using recent results of He et al. [J. High Energy Phys. 05 (2015) 106], this construction, first done by Emparan [arXiv:hep-th/9412003], can be put on much firmer ground. We generalize to type II and heterotic superstrings and demonstrate modular invariance. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration close to the black hole horizon. Ultimately, since these partition functions are only part of the full story, divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the higher-spin fields in the string spectrum. We comment on the relevance of this to Solodukhin's recent proposal [Phys. Rev. D 91, 084028 (2015)]. A possible link with the firewall paradox is apparent.
One-loop partition functions of 3D gravity
We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over 'boundary excitations' of AdS3, which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.
Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions
Wilson, Blake A; Gelb, Lev D; Nielsen, Steven O
2015-10-21
Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions. PMID:26493898
Wilson, Blake A.; Nielsen, Steven O. [Department of Chemistry, University of Texas at Dallas, Richardson, Texas 75080 (United States); Gelb, Lev D. [Department of Materials Science and Engineering, University of Texas at Dallas, Richardson, Texas 75080 (United States)
2015-10-21
Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions.
Grand canonical potential of a magnetized neutron gas
Diener, Jacobus P W
2015-01-01
We compute the effective action for stationary and spatially constant magnetic fields, when coupled anomalously to charge neutral fermions, by integrating out the fermions. From this the grand canonical partition function and potential of the fermions and fields are computed. This also takes care of magnetic field dependent vacuum corrections to the grand canonical potential. Possible applications to neutron stars are indicated.
Identification of plasmid partition function in coryneform bacteria.
Kurusu, Y; Satoh, Y.; Inui, M.; Kohama, K; Kobayashi, M.; Terasawa, M.; Yukawa, H
1991-01-01
We have identified and characterized a partition function that is required for stable maintenance of plasmids in the coryneform bacteria Brevibacterium flavum MJ233 and Corynebacterium glutamicum ATCC 31831. This function is localized to a HindIII-NspV fragment (673 bp) adjacent to the replication region of the plasmid, named pBY503, from Brevibacterium stationis IFO 12144. The function was independent of copy number control and was not associated directly with plasmid replication functions. ...
Popovas, Andrius
2016-01-01
Aims. In this work we rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods. Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H$_2$ . Both equilibrium and normal hydrogen was taken into consideration. Results. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hyd...
Partitions, rooks, and symmetric functions in noncommuting variables
Can, Mahir Bilen
2010-01-01
Let $\\Pi_n$ denote the set of all set partitions of $\\{1,2,\\ldots,n\\}$. We consider two subsets of $\\Pi_n$, one connected to rook theory and one associated with symmetric functions in noncommuting variables. Let $\\cE_n\\sbe\\Pi_n$ be the subset of all partitions corresponding to an extendable rook (placement) on the upper-triangular board, $\\cT_{n-1}$. Given $\\pi\\in\\Pi_m$ and $\\si\\in\\Pi_n$, define their {\\it slash product\\/} to be $\\pi|\\si=\\pi\\cup(\\si+m)\\in\\Pi_{m+n}$ where $\\si+m$ is the partition obtained by adding $m$ to every element of every block of $\\si$. Call $\\tau$ {\\it atomic\\/} if it can not be written as a nontrivial slash product and let $\\cA_n\\sbe\\Pi_n$ denote the subset of atomic partitions. Atomic partitions were first defined by Bergeron, Hohlweg, Rosas, and Zabrocki during their study of $NCSym$, the symmetric functions in noncommuting variables. We show that, despite their very different definitions, $\\cE_n=\\cA_n$ for all $n\\ge0$. Furthermore, we put an algebra structure on the formal vector s...
Zeta Function Expression of Spin Partition Functions on Thermal AdS3
Floyd L.Williams
2015-07-01
Full Text Available We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.
Two loop partition function in (compactified) heterotic string vacua
Two loop partition function for the heterotic string theory, compactified on any background preserving space-time supersymmetry at the string tree level, is explicitly calculated. This includes E8 x E8 or SO(32) heterotic string theory in ten dimensional flat space-time
Quantization of the canonical tensor model and an exact wave function
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints provides an algebraically consistent way of discretizing the Dirac algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt quantization of the canonical tensor model. Formally one can obtain wave functions of the ''universe'' by solving the partial differential equations representing the constraints. For the simplest non-trivial case, the unique wave function is exactly and globally obtained. Although this case is far from being realistic, the wave function is physically interesting; locality is favored, and there exists a locus of configurations with features of the beginning of the universe
Canonical self-affine tilings by iterated function systems
Pearse, Erin P. J.
2006-01-01
An iterated function system $\\Phi$ consisting of contractive similarity mappings has a unique attractor $F \\subseteq \\mathbb{R}^d$ which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling $\\mathcal{T}$ of the convex hull of the attractor. More precisely, it tiles the complement of the attractor within its convex hull. These tiles form a collection of sets whose geometry is typically ...
$q$-Virasoro modular double and 3d partition functions
Nedelin, Anton; Zabzine, Maxim
2016-01-01
We study partition functions of 3d $\\mathcal{N}=2$ U(N) gauge theories on compact manifolds which are $S^1$ fibrations over $S^2$. We show that the partition functions are free field correlators of vertex operators and screening charges of the $q$-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL(2,$\\mathbb{Z}$)-related commuting sets of $q$-Virasoro constraints. We generalize our construction to 3d $\\mathcal{N}=2$ unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.
Identification of plasmid partition function in coryneform bacteria
Kurusu, Yasurou; Satoh, Yukie; Inui, Masayuki; Kohama, Keiko; Kobayashi, Miki; Terasawa, Masato; Yukawa, Hideaki (Mitsubishi Petrochemical Co., Ltd., Ibaraki (Japan))
1991-03-01
The authors have identified and characterized a partition function that is required for stable maintenance of plasmids in the coryneform bacteria Brevibacterium flavum MJ233 and Corynebacterium glutamicum ATCC 31831. This function is localized to a HindIII-NspV fragment (673 bp) adjacent to the replication region of the plasmid, named pBY503, from Brevibacterium stationis IFO 12144. The function was independent of copy number control and was not associated directly with plasmid replication functions. This fragment was able to stabilize the unstable plasmids in cis but not in trans.
\\beta-deformed matrix model and Nekrasov partition function
Nishinaka, Takahiro
2011-01-01
We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional \\mathcal{N}=2, SU(2) supersymmetric gauge theories with N_F=2,3 and 4. By evaluating the resolvent using the loop equation for general \\beta, we explicitly construct the first half-genus correction to the free energy and demonstrate the result coincides with the corresponding Nekrasov partition function with general \\Omega-background, including higher instanton contributions after modifying the relation of the Coulomb branch parameter with the filling fraction. Our approach complements the proof using the Selberg integrals directly which is useful to find the contribution in the series of instanton numbers for a given deformation parameter.
β-deformed matrix model and Nekrasov partition function
Nishinaka, Takahiro; Rim, Chaiho
2012-02-01
We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional mathcal{N} = {2} , SU(2) supersymmetric gauge theories with N F = 2 , 3 and 4. By evaluating the resolvent using the loop equation for general β, we explicitly construct the first half-genus correction to the free energy and demonstrate the result coincides with the corresponding Nekrasov partition function with general Ω-background, including higher instanton contributions after modifying the relation of the Coulomb branch parameter with the filling fraction. Our approach complements the proof using the Selberg integrals directly which is useful to find the contribution in the series of instanton numbers for a given deformation parameter.
Unified approach to partition functions of RNA secondary structures.
Bundschuh, Ralf
2014-11-01
RNA secondary structure formation is a field of considerable biological interest as well as a model system for understanding generic properties of heteropolymer folding. This system is particularly attractive because the partition function and thus all thermodynamic properties of RNA secondary structure ensembles can be calculated numerically in polynomial time for arbitrary sequences and homopolymer models admit analytical solutions. Such solutions for many different aspects of the combinatorics of RNA secondary structure formation share the property that the final solution depends on differences of statistical weights rather than on the weights alone. Here, we present a unified approach to a large class of problems in the field of RNA secondary structure formation. We prove a generic theorem for the calculation of RNA folding partition functions. Then, we show that this approach can be applied to the study of the molten-native transition, denaturation of RNA molecules, as well as to studies of the glass phase of random RNA sequences. PMID:24177391
High-Temperature Expansion of Supersymmetric Partition Functions
Ardehali, Arash Arabi; Szepietowski, Phillip
2015-01-01
Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature ($\\beta \\rightarrow 0$) behavior of supersymmetric partition functions $Z^{SUSY}(\\beta)$. Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular, we see that the high-temperature expansion of $\\ln Z^{SUSY}(\\beta)$ terminates at order $\\beta^0$. We also demonstrate how their formula must be modified when applied to SU($N$) toric quiver gauge theories in the planar ($N \\rightarrow \\infty$) limit. Our method for regularizing the one-loop determinants of chiral and vector multiplets helps to clarify the relation between the 4d $\\mathcal{N} = 1$ superconformal index and its corresponding supersymmetric partition function obtained by path-integration.
Computing black hole partition functions from quasinormal modes
Arnold, Peter; Vaman, Diana
2016-01-01
We propose a method of computing one-loop determinants in black hole spacetimes (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in [1]. A necessary ingredient is a refined regularization scheme to regulate the contributions of individual fixed-momentum sectors to the partition function. To this end, we formulate an effective two-dimensional problem in which a natural refinement of standard heat kernel techniques can be used to account for contributions to the partition function at fixed momentum. We test our method in a concrete case by reproducing the scalar one-loop determinant in the BTZ black hole background. We then discuss the application of such techniques to more complicated spacetimes.
The Partition Function of Multicomponent Log-Gases
Sinclair, Christopher D
2012-01-01
We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\\beta} = 1 and {\\beta} = 4) ensembles extended to multicomponent ensembles.
Factorized domain wall partition functions in trigonometric vertex models
Foda, O; Zuparic, M
2007-01-01
We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: 1. The N-state Deguchi-Akutsu models, for N = {2, 3, 4} (and conjecture the result for all N >= 5), and 2. The sl(r+1|s+1) Perk-Schultz models, for {r, s = \\N}, where (given the symmetries of these models) the result is independent of {r, s}.
Factorized domain wall partition functions in trigonometric vertex models
Foda, O.; Wheeler, M.; Zuparic, M.
2007-10-01
We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: (1) the N-state Deguchi Akutsu models, for N \\in \\{2, 3, 4\\} (and conjecture the result for all N>=5), and (2) the sl(r+1|s+1) Perk Schultz models, for \\{r, s \\in \\mathbb {N}\\} , where (given the symmetries of these models) the result is independent of {r,s}.
Anyonic partition functions and windings of planar Brownian motion
The computation of the N-cycle Brownian paths contribution FN(α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that FN0(α)=product k=1N-1[1-(N/k)α]. In the paramount three-anyon case, one can show that F3(α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S3
Conformal transformations and the SLE partition function martingale
Bauer, Michel; Bernard, Denis
2003-01-01
We present an implementation in conformal field theory (CFT) of local finite conformal transformations fixing a point. We give explicit constructions when the fixed point is either the origin or the point at infinity. Both cases involve the exponentiation of a Borel subalgebra of the Virasoro algebra. We use this to build coherent state representations and to derive a close analog of Wick's theorem for the Virasoro algebra. This allows to compute the conformal partition function in non trivia...
High-temperature asymptotics of supersymmetric partition functions
Ardehali, Arash Arabi
2015-01-01
We study the partition function of 4d supersymmetric gauge theories with an R-symmetry on Euclidean $S^3\\times S_\\beta^1$, with $S^3$ the unit-radius squashed three-sphere, and $\\beta$ the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around $S_\\beta^1$. At high temperatures ($\\beta\\to 0$, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If...
Some bounds on quantum partition functions by path-integral methods
Equilibrium statistical mechanics requires the competition of the partition function. The density matrix and hence the quantum partition function may be expressed as an integral with an integral which can be given explicitly, namely as a (Wiener-) path integral. Techniques especially designed for path integrals provide inequalities for density matrices, partition functions and spectral densities. Some of these inequalities related to density matrices and partition functions are reviewed in this paper. 39 refs
Generalised partition functions: inferences on phase space distributions
Treumann, Rudolf A.; Baumjohann, Wolfgang
2016-06-01
It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.
Getting full control of canonical correlation analysis with the AutoBiplot.CCA function
Alves, M. Rui
2016-06-01
Function AutoBiplot.CCA was built in R language. Given two multivariate data sets, this function carries out a conventional canonical correlation analysis, followed by the automatic production of predictive biplots based on the accuracy of readings as assessed by a mean standard predictive error and a user defined tolerance value. As the user's intervention is mainly restricted to the choice of the magnitude of the t.axis value, common misinterpretations, overestimations and adjustments between outputs and personal beliefs are avoided.
Catoni, Francesco; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Funzione Centrale INFO; Nichelatti, Enrico [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Innovazione
1997-10-01
Systems of two-dimensional hypercomplex numbers are usually studied in their canonical form, i.e. according to the multiplicative rule for the ``imaginary``versor i{sup 2} = {+-} 1, 0. In this report those systems for which i{sup 2} = {alpha} + {beta}i are studied and expressions are derived for functions given by series expansion as well as for some elementary functions. The results obtained for systems which can be decomposed are then extended to all systems.
Random trees between two walls: exact partition function
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labelled by integers representing their position in the target space, with the solid-on-solid constraint that adjacent vertices have labels differing by ±1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p function with constrained periods. These results are used to analyse the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs
1 Taiwo O. A
2013-01-01
The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with thos...
Semiclassical partition function for the double-well potential
Kroff, D; de Carvalho, C A A; Fraga, E S; Jorás, S E
2013-01-01
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the non-perturbative framework of the boundary effective theory.
Non-perturbative Nekrasov partition function from string theory
We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3×T2 and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general Ω-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of [1] and provides further evidence for our proposal of a string theory realisation of the Ω-background
Holographic partition functions and phases for higher genus Riemann surfaces
Maxfield, Henry; Ross, Simon F.; Way, Benson
2016-06-01
We describe a numerical method to compute the action of Euclidean saddle points for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.
Ratios of partition functions for the log-gamma polymer
Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo; Yilmaz, Atilla
2015-01-01
The Annals of Probability 2015, Vol. 43, No. 5, 2282–2331 DOI: 10.1214/14-AOP933 © Institute of Mathematical Statistics, 2015 RATIOS OF PARTITION FUNCTIONS FOR THE LOG-GAMMA POLYMER BY NICOS GEORGIOU1, FIRAS RASSOUL-AGHA1, TIMO SEPPÄLÄINEN2 AND ATILLA YILMAZ3 University of Sussex, University of Utah, University of Wisconsin–Madison and Bo˘gaziçi University We introduce a random walk in random environment associated to an underlying directed polymer model in 1 ...
Holographic partition functions and phases for higher genus Riemann surfaces
Maxfield, Henry; Way, Benson
2016-01-01
We describe a numerical method to compute the action of Euclidean saddlepoints for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.
Anyonic Partition Functions and Windings of Planar Brownian Motion
Desbois, Jean; Heinemann, Christine; Ouvry, Stéphane
1994-01-01
The computation of the $N$-cycle brownian paths contribution $F_N(\\alpha)$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\\alpha)= \\prod_{k=1}^{N-1}(1-{N\\over k}\\alpha)$. In the paramount $3$-anyon case, one can show that $F_3(\\alpha)$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.
Canonical and alternate functions of the microRNA biogenesis machinery.
Chong, Mark M W; Zhang, Guoan; Cheloufi, Sihem; Neubert, Thomas A; Hannon, Gregory J; Littman, Dan R
2010-09-01
The canonical microRNA (miRNA) biogenesis pathway requires two RNaseIII enzymes: Drosha and Dicer. To understand their functions in mammals in vivo, we engineered mice with germline or tissue-specific inactivation of the genes encoding these two proteins. Changes in proteomic and transcriptional profiles that were shared in Dicer- and Drosha-deficient mice confirmed the requirement for both enzymes in canonical miRNA biogenesis. However, deficiency in Drosha or Dicer did not always result in identical phenotypes, suggesting additional functions. We found that, in early-stage thymocytes, Drosha recognizes and directly cleaves many protein-coding messenger RNAs (mRNAs) with secondary stem-loop structures. In addition, we identified a subset of miRNAs generated by a Dicer-dependent but Drosha-independent mechanism. These were distinct from previously described mirtrons. Thus, in mammalian cells, Dicer is required for the biogenesis of multiple classes of miRNAs. Together, these findings extend the range of function of RNaseIII enzymes beyond canonical miRNA biogenesis, and help explain the nonoverlapping phenotypes caused by Drosha and Dicer deficiency. PMID:20713509
Minimal models on Riemann surfaces: The partition functions
Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)
1990-06-04
The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).
Minimal models on Riemann surfaces: The partition functions
The Coulomb gas representation of the An series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius)2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)
Colour-independent partition functions in coloured vertex models
Foda, O., E-mail: omar.foda@unimelb.edu.au [Dept. of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 (Australia); Wheeler, M., E-mail: mwheeler@lpthe.jussieu.fr [Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 (France); Université Pierre et Marie Curie – Paris 6, 4 place Jussieu, 75252 Paris cedex 05 (France)
2013-06-11
We study lattice configurations related to S{sub n}, the scalar product of an off-shell state and an on-shell state in rational A{sub n} integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A{sub n} models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S{sub 2} (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S{sub 2}, which depends on two sets of Bethe roots, {b_1} and {b_2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b_1}→∞, and/or {b_2}→∞, into a product of determinants, 2. Each of the latter determinants is an A{sub 1} vertex-model partition function.
Colour-independent partition functions in coloured vertex models
We study lattice configurations related to Sn, the scalar product of an off-shell state and an on-shell state in rational An integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric An models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S2 (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S2, which depends on two sets of Bethe roots, {b1} and {b2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b1}→∞, and/or {b2}→∞, into a product of determinants, 2. Each of the latter determinants is an A1 vertex-model partition function
On entire functions restricted to intervals, partition of unities, and dual Gabor frames
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2014-01-01
Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire...... functions that lead to a partition of unity in this way, and we provide characterizations of the “cut-off” entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity...
Modular invariant partition function of critical dense polymers
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin–Kasteleyn random cluster models. Starting with a cylinder, the commuting periodic single-row transfer matrices are built from the periodic Temperley–Lieb algebra extended by the shift operators Ω±1. In this enlarged algebra, the non-contractible loop fugacity is α and the contractible loop fugacity is β. The torus is formed by gluing the top and bottom of the cylinder. This gives rise to a variety of non-contractible loops winding around the torus. Because of their nonlocal nature, the standard matrix trace does not produce the proper geometric torus. Instead, we introduce a modified matrix trace for this purpose. This is achieved by using a representation of the enlarged periodic Temperley–Lieb algebra with a parameter v that keeps track of the winding of defects on the cylinder. The transfer matrix representatives and their eigenvalues thus depend on v. The modified trace is constructed as a linear functional on planar connectivity diagrams in terms of matrix traces Trd (with a fixed number of defects d) and Chebyshev polynomials of the first kind. For critical dense polymers, where β=0, the transfer matrix eigenvalues are obtained by solving a functional equation in the form of an inversion identity. The solution depends on d and is subject to selection rules which we prove. Simplifications occur if all non-contractible loop fugacities are set to α=2 in which case the traces are evaluated at v=1. In the continuum scaling limit, the corresponding conformal torus partition function obtained from finite-size corrections agrees with the known modular invariant partition function of symplectic fermions
Hemisphere Partition Function and Analytic Continuation to the Conifold Point
Knapp, Johanna; Scheidegger, Emanuel
2016-01-01
We show that the hemisphere partition function for certain U(1) gauged linear sigma models (GLSMs) with D-branes is related to a particular set of Mellin-Barnes integrals which can be used for analytic continuation to the singular point in the K\\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY) projective hypersurface. We directly compute the analytic continuation of the full quantum corrected central charge of a basis of geometric D-branes from the large volume to the singular point. In the mirror language this amounts to compute the analytic continuation of a basis of periods on the mirror CY to the conifold point. However, all calculations are done in the GLSM and we do not have to refer to the mirror CY. We apply our methods explicitly to the cubic, quartic and quintic CY hypersurfaces.
Twists of Pl\\"ucker coordinates as dimer partition functions
Scott, Jeanne
2013-01-01
The homogeneous coordinate ring of the Grassmannian Gr(k,n) has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Pl\\"ucker coordinates. We introduce a twist map on Gr(k,n) related to the BZ-twist, and give an explicit Laurent expansion for the twist of an arbitrary Pl\\"ucker coordinate, in terms of the cluster variables associated with a fixed Postnikov diagram. The expansion arises as a (scaled) dimer partition function of a weighted version of the bipartite graph dual to the Postnikov diagram, modified by a boundary condition determined by the Pl\\"ucker coordinate.
1 Taiwo O. A
2013-01-01
Full Text Available The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with those obtained by Adomian Decomposition method. It is also observed that the new method is an effective method with high accuracy. Some examples are given to illustrate the method.
Partition Function of 1-, 2-, and 3-D Monatomic Ideal Gas (a Simple and Comprehensive Review)
Khotimah, Siti Nurul
2011-01-01
This article discusses partition function of monatomic ideal gas which is given in Statistical Physisc at Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia. Students in general are not familiar with partition function. This unfamiliarness was detected at a problem of partition function which was re-given in an examination in other dimensions that had been previously given in the lecture. Based on this observation, the need of a simple but comprehensive article about partition function in one-, two-, and three-dimensions is a must. For simplicity, a monatomic ideal gas is chosen.
Natural Microbial Assemblages Reflect Distinct Organismal and Functional Partitioning
Wilmes, P.; Andersson, A.; Kalnejais, L. H.; Verberkmoes, N. C.; Lefsrud, M. G.; Wexler, M.; Singer, S. W.; Shah, M.; Bond, P. L.; Thelen, M. P.; Hettich, R. L.; Banfield, J. F.
2007-12-01
The ability to link microbial community structure to function has long been a primary focus of environmental microbiology. With the advent of community genomic and proteomic techniques, along with advances in microscopic imaging techniques, it is now possible to gain insights into the organismal and functional makeup of microbial communities. Biofilms growing within highly acidic solutions inside the Richmond Mine (Iron Mountain, Redding, California) exhibit distinct macro- and microscopic morphologies. They are composed of microorganisms belonging to the three domains of life, including archaea, bacteria and eukarya. The proportion of each organismal type depends on sampling location and developmental stage. For example, mature biofilms floating on top of acid mine drainage (AMD) pools exhibit layers consisting of a densely packed bottom layer of the chemoautolithotroph Leptospirillum group II, a less dense top layer composed mainly of archaea, and fungal filaments spanning across the entire biofilm. The expression of cytochrome 579 (the most highly abundant protein in the biofilm, believed to be central to iron oxidation and encoded by Leptospirillum group II) is localized at the interface of the biofilm with the AMD solution, highlighting that biofilm architecture is reflected at the functional gene expression level. Distinct functional partitioning is also apparent in a biological wastewater treatment system that selects for distinct polyphosphate accumulating organisms. Community genomic data from " Candidatus Accumulibacter phosphatis" dominated activated sludge has enabled high mass-accuracy shotgun proteomics for identification of key metabolic pathways. Comprehensive genome-wide alignment of orthologous proteins suggests distinct partitioning of protein variants involved in both core-metabolism and specific metabolic pathways among the dominant population and closely related species. In addition, strain- resolved proteogenomic analysis of the AMD biofilms
Elliptic solid-on-solid model's partition function as a single determinant
Galleas, W
2016-01-01
In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the model's partition function.
Smoothed analysis of partitioning algorithms for Euclidean functionals
Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra; Dehne, F.; Iacono, J.; Sack, J.-R.
2011-01-01
Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. We develop a general framework for the application of smoothed analysis to partitioning algorithms for Euclidean optimization problems.
Smoothed analysis of partitioning algorithms for Euclidean functionals
Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra
2013-01-01
Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. In order to explain this performance, we develop a general framework for the application of smoothed analysis to partitioning algorithm
Large N techniques for Nekrasov partition functions and AGT conjecture
Bourgine, Jean-Emile
2013-01-01
The AGT conjecture relates \\mathcal{N}=2 4d SUSY gauge theories to 2d CFTs. Matrix model techniques can be used to investigate both sides of this relation. The large N limit refers here to the size of Young tableaux in the expression of the gauge theory partition function. It corresponds to vanishing of Omega-background equivariant deformation parameters, and should not be confused with the t'Hooft expansion at large number of colors. In the first part of the paper, a saddle point approach is employed to study the Nekrasov-Shatshvili limit of the gauge theory, leading to define beta-deformed, or quantized, Seiberg-Witten curve and differential form. In a second part, this formalism is compared to the large N limit of the Dijkgraaf-Vafa beta-ensemble. A transformation law relating the wave functions appearing at both sides of the conjecture is proposed. It implies a transformation of the Seiberg-Witten 1-form in agreement with the definition proposed earlier. As a side result, a remarkable property of the \\mat...
Partition function and base pairing probabilities of RNA heterodimers
Stadler Peter F
2006-03-01
Full Text Available Abstract Background RNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms. Methods The standard dynamic programming algorithms for computing secondary structures of linear single-stranded RNA molecules are extended to the co-folding of two interacting RNAs. Results We present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures. Availability RNAcofold is distributed as part of the Vienna RNA Package, http://www.tbi.univie.ac.at/RNA/. Contact Stephan H. Bernhart – berni@tbi.univie.ac.at
Polymer quantization and the saddle point approximation of partition functions
Técotl, Hugo A Morales; Rastgoo, Saeed
2015-01-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method can not be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counter-term to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counter-term method. This type of quantization for mechanical models is motivated by the loop quantization of gravity which is known to play a role in the thermodynamics of black holes systems. The model we consider is a non relativistic particle in an i...
Colour-independent partition functions in coloured vertex models
Foda, O
2013-01-01
We study lattice configurations related to S_n, the scalar product of an off-shell state and an on-shell state in rational A_n integrable vertex models, n = {1, 2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A_n models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S_2 [1, 2]. Namely, 1. S_2 which depends on two sets of Bethe roots, b_1 and b_2, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit b_1 -> infinity, and/or b_2 -> infinity, into a product of determinants, 2. Each of the la...
Partition functions for a canonical and microcanonical ensemble are developed which are then used to describe various properties of excited hadronic systems. Relating multinomial coefficients to a generating function of these partition functions, it is shown that the average value of various moments of cluster sizes are of a quite simple form in terms of canonical partition functions. Specific applications of the results are to partitioning problems as in the partitioning of nucleons into clusters arising from a nuclear collision and to branching processes as in Furry branching. The underlying dynamical evolution of a system is studied by parametrizing the multinomial variables of the theory. A Fokker-Planck equation can be obtained from these evolutionary equations. By relating the parameters and variables of the theory to thermodynamic variables, the thermal properties of excited hadronic systems are studied
Polymer quantization and the saddle point approximation of partition functions
Morales-Técotl, Hugo A.; Orozco-Borunda, Daniel H.; Rastgoo, Saeed
2015-11-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method cannot be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counterterm to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counterterm method. This type of quantization for mechanical models is motivated by the loop quantization of gravity, which is known to play a role in the thermodynamics of black hole systems. The model we consider is a nonrelativistic particle in an inverse square potential, and we analyze two polarizations of the polymer quantization in which either the position or the momentum is discrete. In the former case, Thiemann's regularization is applied to represent the inverse power potential, but we still need to incorporate the Hamilton-Jacobi counterterm, which is now modified by polymer corrections. In the latter, momentum discrete case, however, such regularization could not be implemented. Yet, remarkably, owing to the fact that the position is bounded, we do not need a Hamilton-Jacobi counterterm in order to have a well-defined saddle point approximation. Further developments and extensions are commented upon in the discussion.
Inverse structure functions in the canonical wind turbine array boundary layer
Viggiano, Bianca; Gion, Moira; Ali, Naseem; Tutkun, Murat; Cal, Raúl Bayoán
2015-11-01
Insight into the statistical behavior of the flow past an array of wind turbines is useful in determining how to improve power extraction from the overall available energy. Considering a wind tunnel experiment, hot-wire anemometer velocity signals are obtained at the centerline of a 3 x 3 canonical wind turbine array boundary layer. Two downstream locations are considered referring to the near- and far-wake, and 21 vertical points were acquired per profile. Velocity increments are used to quantify the ordinary and inverse structure functions at both locations and their relationship between the scaling exponents is noted. It is of interest to discern if there is evidence of an inverted scaling. The inverse structure functions will also be discussed from the standpoint of the proximity to the array. Observations will also address if inverted scaling exponents follow a power law behavior and furthermore, extended self-similarity of the second moment is used to obtain the scaling exponent of other moments. Inverse structure functions of moments one through eight are tested via probability density functions and the behavior of the negative moment is investigated as well. National Science Foundation-CBET-1034581.
Creativity and Brain-Functioning in Product Development Engineers: A Canonical Correlation Analysis
Travis, Frederick; Lagrosen, Yvonne
2014-01-01
This study used canonical correlation analysis to explore the relation among scores on the Torrance test of figural and verbal creativity and demographic, psychological and physiological measures in Swedish product-development engineers. The first canonical variate included figural and verbal flexibility and originality as dependent measures and…
Partition and Correlation Functions of a Freely Crossed Network Using Ising Model-Type Interactions
Saito, Akira
2016-01-01
We set out to determine the partition and correlation functions of a network under the assumption that its elements are freely connected, with an Ising model-type interaction energy associated with each connection. The partition function is obtained from all combinations of loops on the free network, while the correlation function between two elements is obtained based on all combinations of routes between these points, as well as all loops on the network. These functions allow measurement of the dynamics over the whole of any network, regardless of its form. Furthermore, even as parts are added to the network, the partition and correlation functions can still be obtained. As an example, we obtain the partition and correlation functions in a crystal system under the repeated addition of fixed parts.
Recursive method for the Nekrasov partition function for classical Lie groups
The Nekrasov partition function for supersymmetric gauge theories with general Lie groups is, so far, not known in a closed form, while there is a definition in terms of the integral. In this paper, as an intermediate step to derive the closed form, we give a recursion formula among partition functions, which can be derived from the integral. We apply the method to a toy model that reflects the basic structure of partition functions for BCD-type Lie groups and obtain a closed expression for the factor associated with the generalized Young diagram
Relations between canonical and non-canonical inflation
Gwyn, Rhiannon [Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany); Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2012-12-15
We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field {phi}. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term X in the effective Lagrangian p(X,{phi}) and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.
Relations between canonical and non-canonical inflation
We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field φ. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term X in the effective Lagrangian p(X,φ) and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.
On partition function and Weyl anomaly of conformal higher-spin fields
We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2) partition function. We compute the corresponding spin s Weyl anomaly coefficients as and cs. Our result for as reproduces the expression found recently in (arXiv:1306.5242) by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S4 to a ratio of known partition functions of massless higher-spin field in AdS5 with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in (arXiv:1306.5242) that the sum of the bosonic as coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case
One-loop partition function of three-dimensional flat gravity
Barnich, Glenn; Gonzalez, Hernan A.; Maloney, Alexander; Oblak, Blagoje
2015-01-01
In this note we point out that the one-loop partition function of three-dimensional flat gravity, computed along the lines originally developed for the anti-de Sitter case, reproduces characters of the BMS3 group.
On the domain wall partition functions of level-1 affine so(n) vertex models
Dow, A.; Foda, O.
2006-01-01
We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.
A paradox in the electronic partition function or how to be cautious with mathematics
When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)
Partition function zeros at first-order phase transitions: A general analysis
Biskup, Marek; Borgs, Christian; Chayes, Jennifer T.; Kleinwaks, Logan J.; Kotecky, Roman
2003-01-01
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a companion paper [BBCKK2, math-ph/0304007]. Under these assumptions, we derive equations whose solutions give the location of the zeros of the partition function with periodic boundary conditions, up to an error which we prove is (generically) exponentially small in...
On the analytical evaluation of the partition function for unit hypercubes in four dimensions
The group integrations required for the analytic evaluation of the partition function for unit hypercubes in four dimensions are carried out. Modifications of the graphical rules for SU2 group integrations cited in the literature are developed for this purpose. A complete classification of all surfaces that can be embedded in the unit hypercube is given and their individual contribution to the partition function worked out. Applications are discussed briefly. (orig.)
The partition function of the trigonometric SOS model with a reflecting end
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of the sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms. (letter)
LETTER: The partition function of the trigonometric SOS model with a reflecting end
Filali, G.; Kitanine, N.
2010-06-01
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of the sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Computing the partition function for perfect matchings in a hypergraph
Barvinok, Alexander
2010-01-01
Given non-negative weights w_S on the k-subsets S of a km-element set V, we consider the sum of the products w_{S_1} ... w_{S_m} for all partitions V = S_1 cup ... cup S_m into pairwise disjoint k-subsets S_i. When the weights w_S are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor. In the process, we obtain higher-dimensional versions of the van der Waerden and Bregman-Minc bounds for permanents.
One loop partition function in AdS_3/CFT_2
Chen, Bin
2015-01-01
The 1-loop partition function of the handle-body solutions in the AdS$_3$ gravity have been derived some years ago using the heat-kernel and the method of images. In the semiclassical limit, such partition function should correspond to the order $O (c^0)$ part in the partition function of dual conformal field theory on the boundary Riemann surface. The higher genus partition function could be computed by the multi-point functions in the Riemann sphere via sewing prescription. In the large central charge limit, to the leading order of $c$, the multi-point function is further simplified to be a summation over the product of two-point functions, which may form links. Each link is in one-to-one correspondence with the conjugacy class of the Schottky group of the Riemann surface. Moreover, the value of a link is determined by the eigenvalue of the element in the conjugate class. This allows us to reproduce exactly the gravitational 1-loop partition function. The proof can be generalized to the higher spin gravity ...
Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems
Zylka, Christian; Vojta, Guenter
1993-01-01
The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.
Ising model on random networks and the canonical tensor model
We introduce a statistical system on random networks of trivalent vertices for the purpose of studying the canonical tensor model, which is a rank-three tensor model in the canonical formalism. The partition function of the statistical system has a concise expression in terms of integrals, and has the same symmetries as the kinematical ones of the canonical tensor model. We consider the simplest non-trivial case of the statistical system corresponding to the Ising model on random networks, and find that its phase diagram agrees with what is implied by regrading the Hamiltonian vector field of the canonical tensor model with N=2 as a renormalization group flow. Along the way, we obtain an explicit exact expression of the free energy of the Ising model on random networks in the thermodynamic limit by the Laplace method. This paper provides a new example connecting a model of quantum gravity and a random statistical system
Nagesh, Jayashree; Brumer, Paul; Izmaylov, Artur F
2016-01-01
We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory (TD-DFT) framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Stratman-Scuseria-Frisch atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one- and two-electron integrals in the final expressions. The utility of this partitioning approach is demonstrated by examining several excited states of two bichromophoric compounds: 9-((1-naphthyl)-methyl)-anthracene and 4-((2-naphthyl)-methyl)-benzaldehyde. The LOPM is found to provide nontrivial insights into the nature of electronic energy localization that are not accessible using simple density difference analysis.
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Iterating free-field AdS/CFT: higher spin partition function relations
Beccaria, Matteo; Tseytlin, Arkady A.
2016-07-01
We find a simple relation between a free higher spin partition function on the thermal quotient of {{AdS}}d+1 and the partition function of the associated d-dimensional conformal higher spin field defined on the thermal quotient of {{AdS}}d. Starting with a conformal higher spin field defined in {{AdS}}d, one may also associate to with another conformal field in d-1 dimensions, thus iterating AdS/CFT. We observe that in the case of d=4, this iteration leads to a trivial 3d higher spin conformal theory with parity-even non-local action: it describes a zero total number of dynamical degrees of freedom and the corresponding partition function is equal to 1.
Canonical quantization of macroscopic electromagnetism
Philbin, Thomas Gerard
2010-01-01
Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Krame...
A Unified Scheme for Modular Invariant Partition Functions of WZW Models
Abolhassani, M R
1994-01-01
We introuduce a unified method which can be applied to any WZW model at arbitrary level to search systematically for modular invariant physical partition functions. Our method is based essentially on modding out a known theory on group manifold $G$ by a discrete group $\\Gamma$. We apply our method to $\\widehat {su(n)}$ with $n=2,3,4,5,6$, and to $\\widehat {g_2}$ models, and obtain all the known partition functions and some new ones, and give explicit expressions for all of them.
Partition Functions for Diatomic Molecules in Plasmas out of Thermal Equilibrium
Geraldine FAURE
2012-01-01
Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels is assumed in the two calculation methods. The results obtained by two methods are displayed for four sorts of diatomic molecules, 02, N2, OH and NO, that are present in humid air plasmas. The calculation method of density for the electronically excited states is developed. Finally, a method to calculate the partition functions for simulating the non-normalized diatomic spectra is discussed.
Functional Selectivity of CB2 Cannabinoid Receptor Ligands at a Canonical and Noncanonical Pathway.
Dhopeshwarkar, Amey; Mackie, Ken
2016-08-01
The CB2 cannabinoid receptor (CB2) remains a tantalizing, but unrealized therapeutic target. CB2 receptor ligands belong to varied structural classes and display extreme functional selectivity. Here, we have screened diverse CB2 receptor ligands at canonical (inhibition of adenylyl cyclase) and noncanonical (arrestin recruitment) pathways. The nonclassic cannabinoid (-)-cis-3-[2-hydroxy-4-(1,1-dimethylheptyl)phenyl]-trans-4-(3-hydroxypropyl)cyclohexanol (CP55940) was the most potent agonist for both pathways, while the classic cannabinoid ligand (6aR,10aR)-3-(1,1-Dimethylbutyl)-6a,7,10,10a-tetrahydro-6,6,9-trimethyl-6H-dibenzo[b,d]pyran JWH133) was the most efficacious agonist among all the ligands profiled in cyclase assays. In the cyclase assay, other classic cannabinoids showed little [(-)-trans-Δ(9)-tetrahydrocannabinol and (-)-(6aR,7,10,10aR)-tetrahydro-6,6,9-trimethyl-3-(1-methyl-1-phenylethyl)-6H-dibenzo[b,d]pyran-1-ol] (KM233) to no efficacy [(6aR,10aR)-1-methoxy-6,6,9-trimethyl-3-(2-methyloctan-2-yl)-6a,7,10,10a-tetrahydrobenzo[c]chromene(L759633) and (6aR,10aR)-3-(1,1-dimethylheptyl)-6a,7,8,9,10,10a-hexahydro-1-methoxy-6,6-dimethyl-9-methylene-6H-dibenzo[b,d]pyran]L759656. Most aminoalkylindoles, including [(3R)-2,3-dihydro-5-methyl-3-(4-morpholinylmethyl)pyrrolo[1,2,3-de]-1,4-benzoxazin-6-yl]-1-naphthalenyl-methanone, monomethanesulfonate (WIN55212-2), were moderate efficacy agonists. The cannabilactone 3-(1,1-dimethyl-heptyl)-1-hydroxy-9-methoxy-benzo(c)chromen-6-one (AM1710) was equiefficacious to CP55940 to inhibit adenylyl cyclase, albeit with lower potency. In the arrestin recruitment assays, all classic cannabinoid ligands failed to recruit arrestins, indicating a bias toward G-protein coupling for this class of compound. All aminoalkylindoles tested, except for WIN55212-2 and (1-pentyl-1H-indol-3-yl)(2,2,3,3-tetramethylcyclopropyl)-methanone (UR144), failed
Partitioning heritability by functional category using GWAS summary statistics
Finucane, Hilary K.; Bulik-Sullivan, Brendan; Gusev, Alexander;
2015-01-01
Recent work has demonstrated that some functional categories of the genome contribute disproportionately to the heritability of complex diseases. Here we analyze a broad set of functional elements, including cell type–specific elements, to estimate their polygenic contributions to heritability in...... type–specific enrichments, including significant enrichment of central nervous system cell types in the heritability of body mass index, age at menarche, educational attainment and smoking behavior....
Partitioning of minimotifs based on function with improved prediction accuracy.
Sanguthevar Rajasekaran
Full Text Available BACKGROUND: Minimotifs are short contiguous peptide sequences in proteins that are known to have a function in at least one other protein. One of the principal limitations in minimotif prediction is that false positives limit the usefulness of this approach. As a step toward resolving this problem we have built, implemented, and tested a new data-driven algorithm that reduces false-positive predictions. METHODOLOGY/PRINCIPAL FINDINGS: Certain domains and minimotifs are known to be strongly associated with a known cellular process or molecular function. Therefore, we hypothesized that by restricting minimotif predictions to those where the minimotif containing protein and target protein have a related cellular or molecular function, the prediction is more likely to be accurate. This filter was implemented in Minimotif Miner using function annotations from the Gene Ontology. We have also combined two filters that are based on entirely different principles and this combined filter has a better predictability than the individual components. CONCLUSIONS/SIGNIFICANCE: Testing these functional filters on known and random minimotifs has revealed that they are capable of separating true motifs from false positives. In particular, for the cellular function filter, the percentage of known minimotifs that are not removed by the filter is approximately 4.6 times that of random minimotifs. For the molecular function filter this ratio is approximately 2.9. These results, together with the comparison with the published frequency score filter, strongly suggest that the new filters differentiate true motifs from random background with good confidence. A combination of the function filters and the frequency score filter performs better than these two individual filters.
Drinfeld twist and the domain wall partition function of the eight-vertex model
Hao Kun; Chen xi; Shi Kang-Jie; Yang Wen-Li
2011-01-01
With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N × N square lattice with domain wall boundary condition.
On the Definition of the Partition Function in Quantum Regge Calculus
Nishimura, Jun(Department, of, Particle, and, Nuclear, Physics,, Graduate, University, for, Advanced, Studies, (SOKENDAI),, Tsukuba,, Ibaraki, 305-0801,, Japan)
1995-01-01
We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results.
5D partition functions, q-Virasoro systems and integrable spin-chains
Nieri, Fabrizio; Passerini, Filippo; Torrielli, Alessandro
2013-01-01
We analyze N = 1 theories on S5 and S4 x S1, showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We demonstrate that, when the 5d mass parameters are analytically continued to suitable values, the S5 and S4 x S1 partition functions degenerate to those for S3 and S2 x S1. We explain this mechanism via the recently proposed correspondence between 5d partition functions and correlators with underlying q-Virasoro symmetry. From the q-Virasoro 3-point functions, we axiomatically derive a set of associated reflection coefficients, and show they can be geometrically interpreted in terms of Harish-Chandra c-functions for quantum symmetric spaces. We then link these particular c-functions to the types appearing in the Jost functions encoding the asymptotics of the scattering in integrable spin chains, obtained taking different limits of the XYZ model to XXZ-type.
Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies
There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS3, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.
A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms
Verdebout, S; Jönsson, P; Gaigalas, G; Fischer, C Froese; Godefroid, M
2013-01-01
Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the electron correlation effects. The large OB leads to massive configuration state function (CSF) expansions that are difficult to handle. We show that it is possible to relax the orthonormality restriction on the OB and break down the originally large calculations to a set of smaller ones that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The mixing coefficients of the PCFs are fixed from a small generalized eigenvalue problem. The required matrices are computed using a biorthonormal transformation technique. The new method, called partitioned c...
Chikkagoudar, Satish; Roshan, Usman; Livesay, Dennis
2007-01-01
Probalign computes maximal expected accuracy multiple sequence alignments from partition function posterior probabilities. To date, Probalign is among the very best scoring methods on the BAliBASE, HOMSTRAD and OXBENCH benchmarks. Here, we introduce eProbalign, which is an online implementation of the approach. Moreover, the eProbalign web server doubles as an online platform for post-alignment analysis. The heart-and-soul of the post-alignment functionality is the Probalign Alignment Viewer ...
Alcaraz-Pérez, Francisca; García-Castillo, Jesús; García-Moreno, Diana; López-Muñoz, Azucena; Anchelin, Monique; Angosto, Diego; Zon, Leonard I.; Mulero, Victoriano; Cayuela, María L.
2014-02-01
Dyskeratosis congenita (DC) is an inherited disorder with mutations affecting telomerase or telomeric proteins. DC patients usually die of bone marrow failure. Here we show that genetic depletion of the telomerase RNA component (TR) in the zebrafish results in impaired myelopoiesis, despite normal development of haematopoietic stem cells (HSCs). The neutropenia caused by TR depletion is independent of telomere length and telomerase activity. Genetic analysis shows that TR modulates the myeloid-erythroid fate decision by controlling the levels of the master myeloid and erythroid transcription factors spi1 and gata1, respectively. The alteration in spi1 and gata1 levels occurs through stimulation of gcsf and mcsf. Our model of TR deficiency in the zebrafish illuminates the non-canonical roles of TR, and could establish therapeutic targets for DC.
Semenov, Alexander; Zaikin, Oleg
2016-01-01
In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method. PMID:27190753
Missing mass approximations for the partition function of stimulus driven Ising models.
Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon
2013-01-01
Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and N pat the number of unique patterns in the data, contrasting with the O(L2 (N) ) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding. PMID:23898262
Missing Mass Approximations for the Partition Function of Stimulus Driven Ising Models
Robert Haslinger
2013-07-01
Full Text Available Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data. We use use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNN_{pat} where is L the data length, N the number of neurons and N_{pat} the number of unique patterns in the data, contrasting with the O(L2^N complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.
The method of evaluating quantum partition function for the Hubbard model
The method of evaluation of quantum partition function (QPF) in some four fermion models is proposed. The calculations are carried out by the path integral method. The integral is evaluated by introducing the additional fields (called Hubbard-Stratanovich transformation in some models), integration over fermionic variables, and considering the finite-dimensional approximation of rest integral over bosonic fields in the infinite limit. The result can be represented as a sum of the functional derivatives with respect to the arbitrary bosonic field of the quantum partition of free fermionic theory in the external bosonic field. This expression can be treated in a mean field approximation in closed form (the determinants corresponding to the arbitrary external field are substituted by its mean values corresponding to the mean value of the external fields). The quantum partition function is represented as the integral representation of the function. The approximation for the QPF of the free theory is considered, and the corresponding answer for QPF is studied. A convenient perturbation expansion for ln Z is developed. (author). 6 refs, 1 fig
Heat capacity decomposition by partition function zeros for interacting self-avoiding walks
Chen, Chi-Ning; Hsieh, Yu-Hsin; Hu, Chin-Kun
2013-10-01
A novel method based on partition function zeros is developed to demonstrate the additional advantages by considering both loci of partition function zeros and thermodynamical functions associated with them. With this method, the first pair of complex conjugate zeros (first zeros) can be defined without ambiguity and the critical point of a small system can be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and two overlapping phase transitions can be well separated. This method is applied to the interacting self-avoiding walk (ISAW) of homopolymer with N monomers on the simple cubic lattice, which has a collapse transition at a higher temperature and a freezing transition at a low temperature. The exact partition functions ZN with N up to 27 are calculated and our approach gives a clear scenario for the collapse and the freezing transitions.
Partition function of N=2* SYM on a large four-sphere
Hollowood, Timothy J
2015-01-01
We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the theory on R^4. For N an even (odd) integer and \\theta_YM=0, (\\pi), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge [N/2] become massless. We argue that the dyon singularity is the lone saddle point in the SU(2) theory, while for SU(N) with N>2, we characterize potentially competing saddle points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle point and obtain its free energy as a function of g_YM and N, and show that the results are "large-N exact". In the large-N theory our results provide analytical expressions for the pe...
Barklem, Paul S
2016-01-01
Partition functions and dissociation equilibrium constants are presented for 291 diatomic molecules for temperatures in the range from near absolute zero to 10000 K, thus providing data for many diatomic molecules of astrophysical interest at low temperature. The calculations are based on molecular spectroscopic data from the book of Huber and Herzberg with significant improvements from the literature, especially updated data for ground states of many of the most important molecules by Irikura. Dissociation energies are collated from compilations of experimental and theoretical values. Partition functions for 284 species of atoms for all elements from H to U are also presented based on data collected at NIST. The calculated data are expected to be useful for modelling a range of low density astrophysical environments, especially star-forming regions, protoplanetary disks, the interstellar medium, and planetary and cool stellar atmospheres. The input data, which will be made available electronically, also prov...
The 2-loop partition function of large N gauge theories with adjoint matter on S^3
Mussel, Matan
2009-01-01
We compute the 2-loop thermal partition function of Yang-Mills theory on a small 3-sphere, in the large N limit with weak 't Hooft coupling. We include N_s scalars and N_f chiral fermions in the adjoint representation of the gauge group (S)U(N), with arbitrary Yukawa and quartic scalar couplings, assuming only commutator interactions. From this computation one can extract information on the perturbative corrections to the spectrum of the theory, and the correction to its Hagedorn temperature. Furthermore, the computation of the 2-loop partition function is a necessary step towards determining the order of the deconfinement phase transition at weak coupling, for which a 3-loop computation is needed.
We construct polarized spin reversal operator (PSRO) which yields a class of representations for the BCN type of Weyl algebra, and subsequently use this PSRO to find out novel exactly solvable variants of the BCN type of spin Calogero model. The strong coupling limit of such spin Calogero models generates the BCN type of Polychronakos spin chains with PSRO. We derive the exact spectra of the BCN type of spin Calogero models with PSRO and compute the partition functions of the related spin chains by using the freezing trick. We also find out an interesting relation between the partition functions of the BCN type and AN−1 type of Polychronakos spin chains. Finally, we study spectral properties like level density and distribution of spacing between consecutive energy levels for BCN type of Polychronakos spin chains with PSRO
Taormina, Anne
1993-05-01
The representation theory of the doubly extended N=4 superconformal algebra is reviewed. The modular properties of the corresponding characters can be derived, using characters sumrules for coset realizations of these N=4 algebras. Some particular combinations of massless characters are shown to transform as affine SU(2) characters under S and T, a fact used to completely classify the massless sector of the partition function.
An axiomatic characterization of a value for games in partition function form
Hu, Cheng-Cheng; Yang, Yi-You
2010-01-01
An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for n-Person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307317, 1953) to characterize our value. In addition, we discuss a relations...
Abroi, Aare; Ilves, Ivar; Kivi, Sirje; Ustav, Mart
2004-02-01
Recent studies have suggested that the tethering of viral genomes to host cell chromosomes could provide one of the ways to achieve their nuclear retention and partitioning during extrachromosomal maintenance in dividing cells. The data we present here provide firm evidence that the partitioning of the bovine papillomavirus type 1 (BPV1) genome is dependent on the chromatin attachment process mediated by viral E2 protein and its multiple binding sites. On the other hand, the attachment of E2 and the E2-mediated tethering of reporter plasmids to host chromosomes are not necessarily sufficient for efficient partitioning, suggesting that additional E2-dependent activities might be involved in the latter process. The activity of E2 protein in chromatin attachment and partitioning is more sensitive to the point mutations in the N-terminal domain than its transactivation and replication initiation functions. Therefore, at least part of the interactions of the E2 N-terminal domain with its targets during the chromatin attachment and partitioning processes are likely to involve specific receptors not involved in transactivation and replication activities of the protein. The mutational analysis also indicates that the binding of E2 to chromatin is not achieved through interaction of linear N-terminal subsequences of the E2 protein with putative receptors. Instead, the composite surface elements of the N-terminal domain build up the receptor-binding surface of E2. In this regard, the interaction of BPV1 E2 with its chromosomal targets clearly differs from the interactions of LANA1 protein from Kaposi's sarcoma-associated human herpesvirus and EBNA1 from Epstein-Barr virus with their specific receptors. PMID:14747575
By means of the semiempirical quantum chemical MINDO/3- and MNDO-MO-methods it is possible to perform calculations for use in evaluation or interpretation of isotope effects to such an extent that would not be rationally fossible by corresponding experiments. But only the calculated reduced partition function ratios of isotopically substituted molecules can be applied with sufficient reliability for discussions. The temperature dependence of the reduced partition function ratios of over 100 molecules, ions, and radicals regarding the H/D, 12C/13C-, 14N/15N-, 16O/18O-, 28Si/30Si-, 32S/34S-, and 35Cl/37Cl-substitution has been calculated. From these results general conclusions concerning the dependence of isotope effects from the chemical structure of the corresponding molecules have been drawn. In particular, a relationship between the reduced partition function ratio and the electronic charge of the substituted atom has been found. In addition, examples are given for the application of the calculation algorithm used above in connection with combined isotopic substitutions, radical cations, and transition states of chemical reactions. (author)
Geometry of Spin and Spin^c structures in the M-theory partition function
Sati, Hisham
2010-01-01
We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main source of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spin^c case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in ten dimensions, the mod 2 index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the alpha-invariant, which in general depends on the Spin structure. This reveals many interesting connection to positive scalar curvature manifolds and constructions related to the Gromov-Lawson(-Rosenberg) ...
Mcconaghy, Trent; Gielen, Georges
2011-01-01
This paper presents a method to automatically generate compact symbolic performance models of analog circuits with no prior specification of an equation template. The approach takes SPICE simulation data as input, which enables modeling of any nonlinear circuits and circuit characteristics. Genetic programming is applied as a means of traversing the space of possible symbolic expressions. A grammar is specially designed to constrain the search to a canonical form for functions. Novel evolutionary search operators are designed to exploit the structure of the grammar. The approach generates a set of symbolic models which collectively provide a tradeoff between error and model complexity. Experimental results show that the symbolic models generated are compact and easy to understand, making this an effective method for aiding understanding in analog design. The models also demonstrate better prediction quality than posynomials.
VizieR Online Data Catalog: Partition functions for molecules and atoms (Barklem+, 2016)
Barklem, P. S.; Collet, R.
2016-02-01
The results and input data are presented in the following files. Table 1 contains dissociation energies from the literature, and final adopted values, for 291 molecules. The literature values are from the compilations of Huber & Herzberg (1979, Constants of Diatomic Molecules (Van Nostrand Reinhold), Luo (2007, Comprehensive Handbook of Chemical Bond Energies (CRC Press)) and G2 theory calculations of Curtiss et al. (1991, J. Chem. Phys., 94, 7221). Table 2 contains the input data for the molecular calculations including adopted dissociation energy, nuclear spins, molecular spectroscopic constants and their sources. There are 291 files, one for each molecule, labelled by the molecule name. The various molecular spectroscopic constants are as defined in the paper. Table 4 contains the first, second and third ionisation energies for all chemical elements from H to U. The data comes from the CRC Handbook of Chemistry and Physics (Haynes, W.M. 2010, CRC Handbook of Chemistry and Physics, 91st edn. (CRC Press, Taylor and Francis Group)). Table 5a contains a list of keys to bibliographic references for the atomic energy level data that was extracted from NIST Atomic Spectra Database and used in the present work to compute atomic partition functions. The citation keys are abbreviations of the full bibliographic references which are made available in Table 5b in BibTeX format. Table 5b contains the full bibliographic references for the atomic energy level data that was extracted from the NIST Atomic Spectra Database. Table 6 contains tabulated partition function data as a function of temperature for 291 molecules. Table 7 contains tabulated equilibrium constant data as a function of temperature for 291 molecules. Table 8 contains tabulated partition function data as a function of temperature for 284 atoms and ions. The paper should be consulted for further details. (10 data files).
Semiclassical approximation to the partition function of a particle in D dimensions
Aragão de Carvalho, C; Fraga, E S; Jorás, S E
2000-01-01
We use a path integral formalism to derive the semiclassical series for the partition function of a particle in D dimensions. We analyze in particular the case of attractive central potentials, obtaining explicit expressions for the fluctuation determinant and for the semiclassical two-point function in the special cases of the harmonic and single-well quartic anharmonic oscillators. The specific heat of the latter is compared to precise WKB estimates. We conclude by discussing the possible extension of our results to field theories.
Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
Aguilera-Damia, Jeremias; Silva, Guillermo A
2014-01-01
We compute the 1-loop partition function for strings in $AdS_4\\times\\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
Aguilera-Damia, Jeremías; Correa, Diego H.; Silva, Guillermo A.
2015-03-01
We compute the 1-loop partition function for strings in , whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
Russo, Jorge G
2015-01-01
We exactly compute the partition function for $U(2)_k\\times U(2)_{-k}$ ABJM theory on $\\mathbb S^3$ deformed by mass $m$ and Fayet-Iliopoulos parameter $\\zeta $. For $k=1,2$, the partition function has an infinite number of Lee-Yang zeros. For general $k$, in the decompactification limit the theory exhibits a quantum (first-order) phase transition at $m=2\\zeta $.
Geometry of Spin and SPINc Structures in the M-Theory Partition Function
Sati, Hisham
We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta invariants upon variation of the Spin structure. The main sources of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spinc case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in 10 dimensions, the (mod 2) index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the α-invariant, which in general depends on the Spin structure. This reveals many interesting connections to positive scalar curvature manifolds and constructions related to the Gromov-Lawson-Rosenberg conjecture. In the 12-dimensional theory bounding M-theory, we study similar geometric questions, including choices of metrics and obtaining elements of K-theory in 10 dimensions by pushforward in K-theory on the disk fiber. We interpret the latter in terms of the families index theorem for Dirac operators on the M-theory circle and disk. This involves superconnections, eta forms, and infinite-dimensional bundles, and gives elements in Deligne cohomology in lower dimensions. We illustrate our discussion with many examples throughout.
Boundary superstring field theory annulus partition function in the presence of tachyons
We compute the Boundary Superstring Field Theory partition function on the annulus in the presence of independent linear tachyon profiles on the two boundaries. The R-R sector is found to contribute non-trivially to the derivative terms of the space-time effective action. In the process we construct a boundary state description of D-branes in the presence of a linear tachyon. We quantize the open string in a tachyonic background and address the question of open/closed string duality. (author)
Potts Model Partition Functions for Self-Dual Families of Strip Graphs
Chang, Shu-Chiuan; Shrock, Robert
2001-01-01
We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary conditions. The general partition function $Z$ and the T=0 antiferromagnetic special case $P$ (chromatic polynomial) have the respective forms $\\sum_{j=1}^{N_{F,L_y,\\lambda}} c_{F,L_y,j} (\\lambda_{F,L_y,j})^{L_x}$, with $F=Z,P$. For arbitrary $L_y$, we determine (i) the general coefficient $c_{F,L_y,j}$ i...
Chang, Shu-Chiuan; Shrock, Robert
2000-01-01
partial abstract: The $q$-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form $Z(G,q,v)=\\sum_{j=1}^{N_{Z,G,\\lambda}}c_{Z,G,j}(\\lambda_{Z,G,j})^{L_x}$, where $v$ is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ($v=-1$) is the chromatic polynomial $P(G,q)$. Using coloring and transfer matrix methods, we give general formulas for $C_{X,G}=\\sum_{j=1}...
Partition function of a chiral boson on a 2-torus from the Floreanini–Jackiw Lagrangian
We revisit the problem of quantizing a chiral boson on a torus. The conventional approach is to extract the partition function of a chiral boson from the path integral of a non-chiral boson. Instead we compute it directly from the chiral boson Lagrangian of Floreanini and Jackiw modified by topological terms involving an auxiliary field. A careful analysis of the gauge-fixing condition for the extra gauge symmetry reproduces the correct results for the free chiral boson, and has the advantage of being applicable to a wider class of interacting chiral boson theories
Multiple-diglycolamide-functionalized ligands (MDGA) in room temperature ionic liquids (RTILs) were studied for extraction of actinides and lanthanides from aqueous acidic solutions. The extraction kinetics, separation behavior, associated thermodynamics of extraction, nature of the extracted species formed were studied. Luminescence spectroscopy was used to understand the nature of bonding between metal and ligands, formation of inner sphere/outer sphere complex etc. The radiolytic stability of solvent systems was studied and attempt was made to understand the degradation products. Finally, all the systems were evaluated for 'actinide partitioning' from synthetic high level liquid waste solution (HLLW). (author)
Inner products of Bethe states as partial domain wall partition functions
Kostov, Ivan
2012-01-01
We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.
Airy Equation for the Topological String Partition Function in a Scaling Limit
Alim, Murad; Yau, Shing-Tung; Zhou, Jie
2016-04-01
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.
Airy Equation for the Topological String Partition Function in a Scaling Limit
Alim, Murad; Yau, Shing-Tung; Zhou, Jie
2016-06-01
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.
Modular invariant partition functions for non-compact G/Ad(H) models
Bjornsson, Jonas
2010-01-01
We propose a spectrum for a class of gauged non-compact G/Ad(H) WZNW models, including spectrally flowed images of highest, lowest, and mixed extremal weight modules. These are combined into blocks whose characters, due to the Lorentzian signature of the target space, are divergent and treated as formal expressions in need of regularisation. Assuming that this is possible, we show that these extended characters transform linearly under modular transformations, and can be used to write down modular invariant partition functions.
Exact Partition Functions of Interacting Self-Avoiding Walks on Lattices
Hsieh, Yu-Hsin; Chen, Chi-Ning; Hu, Chin-Kun
2016-02-01
Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW) on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping Cυ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.
Exact Partition Functions of Interacting Self-Avoiding Walks on Lattices
Hsieh Yu-Hsin
2016-01-01
Full Text Available Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping Cυ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.
Buchanan, Paul J.; McCloskey, Karen D.
2016-01-01
The importance of ion channels in the hallmarks of many cancers is increasingly recognised. This article reviews current knowledge of the expression of members of the voltage-gated calcium channel family (CaV) in cancer at the gene and protein level and discusses their potential functional roles. The ten members of the CaV channel family are classified according to expression of their pore-forming α-subunit; moreover, co-expression of accessory α2δ, β and γ confers a spectrum of biophysical c...
Akemann, G. [Department of Mathematical Sciences and BURSt Research Centre, School of Information Systems, Computing and Mathematics, Brunel University West London, Uxbridge UB8 3PH (United Kingdom)]. E-mail: gernot.akemann@brunel.ac.uk; Basile, F. [Department of Mathematical Sciences and BURSt Research Centre, School of Information Systems, Computing and Mathematics, Brunel University West London, Uxbridge UB8 3PH (United Kingdom); Dipartimento di Fisica dell' Universita di Pisa and INFN, Via Buonarroti, 56127 Pisa (Italy)
2007-03-26
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal polynomials in the complex plane and their kernel. They are much simpler than the corresponding expressions for symplectic matrix models with real eigenvalues, and we explicitly show how to recover these in the Hermitean limit. This explains the appearance of three different kernels as quaternion matrix elements there in terms of derivatives of a single kernel here.
Barklem, P. S.; Collet, R.
2016-04-01
Partition functions and dissociation equilibrium constants are presented for 291 diatomic molecules for temperatures in the range from near absolute zero to 10 000 K, thus providing data for many diatomic molecules of astrophysical interest at low temperature. The calculations are based on molecular spectroscopic data from the book of Huber & Herzberg (1979, Constants of Diatomic Molecules) with significant improvements from the literature, especially updated data for ground states of many of the most important molecules by Irikura (2007, J. Phys. Chem. Ref. Data, 36, 389). Dissociation energies are collated from compilations of experimental and theoretical values. Partition functions for 284 species of atoms for all elements from H to U are also presented based on data collected at NIST. The calculated data are expected to be useful for modelling a range of low density astrophysical environments, especially star-forming regions, protoplanetary disks, the interstellar medium, and planetary and cool stellar atmospheres. The input data, which will be made available electronically, also provides a possible foundation for future improvement by the community. Full Tables 1-8 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/588/A96
Grand canonical ensemble, multi-particle wave functions and scattering data
Bruckmann, Falk; Kloiber, Thomas; Sulejmanpasic, Tin
2015-01-01
We show that information about scattering data of a quantum field theory can be obtained from studying the system at finite density and low temperatures. In particular we consider models formulated on the lattice which can be exactly dualized to theories of conserved charge fluxes on lattice links. Apart from eliminating the complex action problem at nonzero chemical potential mu, these dualizations allow for a particle world line interpretation of the dual fluxes from which one can extract data about the 2-particle wave function. As an example we perform dual Monte Carlo simulations of the 2-dimensional O(3) model at nonzero mu and finite volume, whose non-perturbative spectrum consists of a massive triplet of particles. At nonzero mu particles are induced in the system, which at sufficiently low temperature give rise to sectors of fixed particle number. We show that the scattering phase shifts can be obtained either from the critical chemical potential values separating the sectors or directly from the wave...
Feldman, Michal; Tennenholtz, Moshe
We introduce partition equilibrium and study its existence in resource selection games (RSG). In partition equilibrium the agents are partitioned into coalitions, and only deviations by the prescribed coalitions are considered. This is in difference to the classical concept of strong equilibrium according to which any subset of the agents may deviate. In resource selection games, each agent selects a resource from a set of resources, and its payoff is an increasing (or non-decreasing) function of the number of agents selecting its resource. While it has been shown that strong equilibrium exists in resource selection games, these games do not possess super-strong equilibrium, in which a fruitful deviation benefits at least one deviator without hurting any other deviator, even in the case of two identical resources with increasing cost functions. Similarly, strong equilibrium does not exist for that restricted two identical resources setting when the game is played repeatedly. We prove that for any given partition there exists a super-strong equilibrium for resource selection games of identical resources with increasing cost functions; we also show similar existence results for a variety of other classes of resource selection games. For the case of repeated games we identify partitions that guarantee the existence of strong equilibrium. Together, our work introduces a natural concept, which turns out to lead to positive and applicable results in one of the basic domains studied in the literature.
The partition function of interfaces from the Nambu-Goto effective string theory
Billo, M; Ferro, L
2006-01-01
We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.
Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing
2015-10-01
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.
Wu, M.-C.; Hu, C.-K. [Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan (China)]. E-mails: mcwu@phys.sinica.edu.tw; huck@phys.sinica.edu.tw
2002-06-28
The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on MxN square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, C/k{sub B}, as a function of temperature, {theta}=k{sub B}T/J. We find that for the NxN sq lattice, C/k{sub B} for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N x N pt and hc lattices, C/k{sub B} for ap, pa and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model. (author)
Partition function expansion on region graphs and message-passing equations
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)
Twists of Plücker Coordinates as Dimer Partition Functions
Marsh, R. J.; Scott, J. S.
2016-02-01
The homogeneous coordinate ring of the Grassmannian Gr k, n has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Plücker coordinates. We introduce a twist map on Gr k, n , related to the Berenstein-Fomin-Zelevinsky-twist, and give an explicit Laurent expansion for the twist of an arbitrary Plücker coordinate in terms of the cluster variables associated with a fixed Postnikov diagram. The expansion arises as a (scaled) dimer partition function of a weighted version of the bipartite graph dual to the Postnikov diagram, modified by a boundary condition determined by the Plücker coordinate. We also relate the twist map to a maximal green sequence.
Stochastic processes with ZN symmetry and complex Virasoro representations. The partition functions
In a previous letter (Alcaraz F C et al 2014 J. Phys. A: Math. Theor. 47 212003) we have presented numerical evidence that a Hamiltonian expressed in terms of the generators of the periodic Temperley–Lieb algebra has, in the finite-size scaling limit, a spectrum given by representations of the Virasoro algebra with complex highest weights. This Hamiltonian defines a stochastic process with a ZN symmetry. We give here analytical expressions for the partition functions for this system which confirm the numerics. For N even, the Hamiltonian has a symmetry which makes the spectrum doubly degenerate leading to two independent stochastic processes. The existence of a complex spectrum leads to an oscillating approach to the stationary state. This phenomenon is illustrated by an example. (fast track communication)
Modular invariant partition functions for the doubly extended N=4 superconformal algebras
Ooguri, Hirosi (Research Inst. for Mathematical Sciences, Kyoto Univ. (Japan) Enrico Fermi Inst., Univ. of Chicago, IL (United States)); Petersen, J.L. (Niels Bohr Inst., Copenhagen (Denmark)); Taormina, A. (Enrico Fermi Inst., Univ. of Chicago, IL (United States))
1992-01-20
Non-trivial modular properties of characters of the doubly extended N=4 superconformal algebras A{sub {gamma}}, A{sub {gamma}} are derived from two different points of view. First, we use realizations on Wolf spaces, in particular when one of the levels of the two commuting affine SU(2) subalgebras takes the value 2. We emphasize how these realizations involve rational torus theories, and how some specific combinations of massless characters transform under the modular group as affine SU(2) characters. Second, we show how these combinations, and generalizations thereof, emerge from a study of the explicit form of the characters when angular variables are partly restricted, but the levels are not. The two results are then combined to give stringent constraints on the modular invariant A{sub {gamma}} partition functions and they give rise to a partial classification of the latter, closely related to that of affine SU(2). (orig.).
Modular invariant partition functions for the doubly extended N = 4 superconformal algebras
Ooguri, Hirosi; Petersen, Jens Lyng; Taormina, Anne
1992-01-01
Non-trivial modular properties of characters of the doubly extended N = 4 superconformal algebras Aγ, Ãγ are derived from two different points of view. First, we use realizations on Wolf spaces, in particular when one of the levels of the two commuting affine SU(2) subalgebras takes the value 2. We emphasize how these realizations involve rational torus theories, and how some specific combinations of massless characters transform under the modular group as affine SU(2) characters. Second, we show how these combinations, and generalizations thereof, emerge from a study of the explicit form of the characters when angular variables are partly restricted, but the levels are not. The two results are then combined to give stringent constraints on the modular invariant Ãγ partition functions and they give rise to a partial classification of the latter, closely related to that of affine SU(2).
Singularities of the Partition Function for the Ising Model Coupled to 2D Quantum Gravity
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2D quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two-matrix model and by Monte-Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.
Restricted Partition Functions and Inverse Energy Cascades in Parity Symmetry Breaking flows
Herbert, Corentin
2014-01-01
When the symmetries of homogenous isotropic turbulent flows are broken, different sets of modes with different physical roles emerge. In particular, choosing a forcing which puts more weight on one or the other of these sets may result in different statistics for the energy transfers. We use the general method of computing a partition function restricted to a portion of phase space to study analytically these different statistics. We illustrate this method in the case of parity symmetry breaking, measured by helicity. It is shown that when helicity is sign definite at all scales, an inverse cascade is expected for the energy. When sign-definiteness is lost, even for a small set of modes, this cascade disappears and there is a sharp phase transition to the standard helical equipartition spectra.
Two-loop partition function in the planar plane-wave matrix model
Spradlin, Marcus; Van Raamsdonk, Mark; Volovich, Anastasia
2004-12-01
We perform two independent calculations of the two-loop partition function for the 't Hooft large N limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU (2 | 4) subsector. We find precise agreement between the results of the two calculations. Various polynomials appearing in the result have rather special properties, possibly related to the large symmetry algebra of the theory or to integrability.
Two-Loop Partition Function in the Planar Plane-Wave Matrix Model
Spradlin, M; Volovich, A; Spradlin, Marcus; Raamsdonk, Mark Van; Volovich, Anastasia
2004-01-01
We perform two independent calculations of the two-loop partition function for the large N 't Hooft limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU(2|4) subsector. We find precise agreement between the results of the two calculations. Various polynomials appearing in the result have rather special properties, possibly related to the large symmetry algebra of the theory or to integrability.
A detailed study of the S-K model through the analysis of the zeros of the partition function in the complex temperature plane is performed. By the exact way, the notable thermodynamical properties of the system to a variety of the length (N=5→25 spins) are calculated, using only standards concepts (without the use of tricks like that of replicas). Dilute models had been also considered. The principal result of this work is the characterization of the zeros of the partition function of the S-K model. (author)
Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach
Jimenez, Kevin; Reslen, Jose
2016-08-01
The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.
Canonical Quantum Statistics of Schwarzschild Black Holes and Ising Droplet Nucleation
Kastrup, H. A.
1997-01-01
Recently is was shown that the imaginary part of the canonical partition function of Schwarzschild black holes with an energy spectrum E_n = \\sigma \\sqrt{n} E_P, n= 1,2, ..., has properties which - naively interpreted - leads to the expected unusual thermodynamical properties of such black holes (Hawking temperature, Bekenstein-Hawking entropy etc). The present paper interprets the same imaginary part in the framework of droplet nucleation theory in which the rate of transition from a metasta...
Partition function, metastability, and kinetics of the escape transition for an ideal chain
Klushin, L. I.; Skvortsov, A. M.; Leermakers, F. A.
2004-06-01
An end-tethered polymer chain squeezed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flower-like conformation partially escaped from the gap. We present a rigorous analytical theory for the equilibrium and kinetic aspects of this phenomenon for a Gaussian chain. Applying the analogy with the problem of the adsorption of an ideal chain constrained by one of its ends, we obtain a closed analytical expression for the exact partition function. Various equilibrium thermodynamic characteristics (the fraction of imprisoned segments, the average compression, and lateral forces) are calculated as a function of the piston separation. The force versus separation curve is studied in two complementary statistical ensembles, the constant force and the constant confinement width ones. The differences in these force curves are significant in the transition region for large systems, but disappear for small systems. The effects of metastability are analyzed by introducing the Landau free energy as a function of the chain stretching, which serves as the order parameter. The phase diagram showing the binodal and two spinodal lines is presented. We obtain the barrier heights between the stable and metastable states in the free energy landscape. The mean first passage time, i.e., the lifetime of the metastable coil and flower states, is estimated on the basis of the Fokker-Planck formalism. Equilibrium analytical theory for a Gaussian chain is complemented by numerical calculations for a lattice freely jointed chain model.
Jonathan Witztum
Full Text Available The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles. We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent, as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life.
Witztum, Jonathan; Persi, Erez; Horn, David; Pasmanik-Chor, Metsada; Chor, Benny
2014-01-01
The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles). We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO) analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent), as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life. PMID:24594619
Pattern-Driven Architectural Partitioning. Balancing Functional and Non-functional Requirements
Harrison, Neil; Avgeriou, Paris
2007-01-01
One of the vexing challenges of software architecture is the problem of satisfying the functional specifications of the system to be created while at the same time meeting its non-functional needs. In this work we focus on the early stages of the software architecture process, when initial high-leve
Partition function on spheres: how (not) to use zeta function regularization
Monin, A
2016-01-01
It is known that not all summation methods are linear and stable. Zeta function regularization is in general non-linear. However, in some cases formal manipulations with "zeta function" regularization (assuming linearity of sums) lead to correct results. We consider several examples and show why this happens.
Zhang, Zhen; Lim, Chae Young; Maiti, Tapabrata; Kato, Seiji
2016-01-01
In climate change study, the infrared spectral signatures of climate change have recently been conceptually adopted, and widely applied to identifying and attributing atmospheric composition change. We propose a Bayesian hierarchical model for spatial clustering of the high-dimensional functional data based on the effects of functional covariates and local features. We couple the functional mixed-effects model with a generalized spatial partitioning method for: (1) producing spatially contigu...
Exact partition functions for the $\\Omega$-deformed $\\mathcal N=2^{*}$ $SU(2)$ gauge theory
Beccaria, Matteo
2016-01-01
We study the low energy effective action of the $\\Omega$-deformed $\\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $\\epsilon_{1},\\epsilon_{2}$, the scalar field expectation value $a$, and the hypermultiplet mass $m$. We explore the plane $(\\frac{m}{\\epsilon_{1}}, \\frac{\\epsilon_{2}}{\\epsilon_{1}})$ looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit $\\epsilon_{2}\\to 0$. We propose a simple condition on the structure of poles of the $k$-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value $a$ and the modular parameter $q$ appearing...
Temperature-dependent nuclear partition functions and abundances in the stellar interior
Nabi, Jameel-Un; Nasser Tawfik, Abdel; Ezzelarab, Nada; Abas Khan, Ali
2016-05-01
We calculate the temperature-dependent nuclear partition functions (TDNPFs) and nuclear abundances for 728 nuclei, assuming nuclear statistical equilibrium (NSE). The theories of stellar evolution support NSE. Discrete nuclear energy levels have been calculated microscopically, using the pn-QRPA theory, up to an excitation energy of 10 MeV in the calculation of the TDNPFs. This feature of our paper distinguishes it from previous calculations. Experimental data is also incorporated wherever available to ensure the reliability of our results. Beyond 10 MeV, we employ a simple Fermi gas model and perform integration over the nuclear level densities to approximate the TDNPFs. We calculate nuclidic abundances, using the Saha equation, as a function of three parameters: stellar density, stellar temperature and the lepton-to-baryon content of stellar matter. All these physical parameters are considered to be extremely important in the stellar interior. The results obtained in this paper show that the equilibrium configuration of nuclei remains unaltered by increasing the stellar density (only the calculated nuclear abundances increase by roughly the same order of magnitude). Increasing the stellar temperature smoothes the equilibrium configuration showing peaks at the neutron-number magic nuclei.
Canonical phylogenetic ordination.
Giannini, Norberto P
2003-10-01
A phylogenetic comparative method is proposed for estimating historical effects on comparative data using the partitions that compose a cladogram, i.e., its monophyletic groups. Two basic matrices, Y and X, are defined in the context of an ordinary linear model. Y contains the comparative data measured over t taxa. X consists of an initial tree matrix that contains all the xj monophyletic groups (each coded separately as a binary indicator variable) of the phylogenetic tree available for those taxa. The method seeks to define the subset of groups, i.e., a reduced tree matrix, that best explains the patterns in Y. This definition is accomplished via regression or canonical ordination (depending on the dimensionality of Y) coupled with Monte Carlo permutations. It is argued here that unrestricted permutations (i.e., under an equiprobable model) are valid for testing this specific kind of groupwise hypothesis. Phylogeny is either partialled out or, more properly, incorporated into the analysis in the form of component variation. Direct extensions allow for testing ecomorphological data controlled by phylogeny in a variation partitioning approach. Currently available statistical techniques make this method applicable under most univariate/multivariate models and metrics; two-way phylogenetic effects can be estimated as well. The simplest case (univariate Y), tested with simulations, yielded acceptable type I error rates. Applications presented include examples from evolutionary ethology, ecology, and ecomorphology. Results showed that the new technique detected previously overlooked variation clearly associated with phylogeny and that many phylogenetic effects on comparative data may occur at particular groups rather than across the entire tree. PMID:14530135
Nimon, Kim; Henson, Robin K.; Gates, Michael S.
2010-01-01
In the face of multicollinearity, researchers face challenges interpreting canonical correlation analysis (CCA) results. Although standardized function and structure coefficients provide insight into the canonical variates produced, they fall short when researchers want to fully report canonical effects. This article revisits the interpretation of…
Singh, Gurpreet; Sharma, Rohit; Singh, Kuldip
2015-09-01
Thermodynamic properties (compressibility coefficient Z γ , specific heat at constant volume c v , adiabatic coefficient γ a , isentropic coefficient γ i s e n , and sound speed c s ) of non-local thermodynamic equilibrium hydrogen thermal plasma have been investigated for different values of pressure and non-equilibrium parameter θ (=Te/Th) in the electron temperature range from 6000 K to 60 000 K. In order to estimate the influence of pressure derivative of partition function on thermodynamic properties, two cases have been considered: (a) in which pressure derivative of partition function is taken into account in the expressions and (b) without pressure derivative of partition function in their expressions. Here, the case (b) represents expressions already available in literature. It has been observed that the temperature from which pressure derivative of partition function starts influencing a given thermodynamic property increases with increase of pressure and non-equilibrium parameter θ. Thermodynamic property in the case (a) is always greater than its value in the case (b) for compressibility coefficient and specific heat at constant volume, whereas for adiabatic coefficient, isentropic coefficient, and sound speed, its value in the case (a) is always less than its value in the case (b). For a given value of θ, the relationship of compressibility coefficient with degree of ionization depends upon pressure in the case (a), whereas it is independent of pressure in the case (b). Relative deviation between the two cases shows that the influence of pressure derivative of partition function is significantly large and increases with the augmentation of pressure and θ for compressibility coefficient, specific heat at constant volume, and adiabatic coefficient, whereas for isentropic coefficient and sound speed, it is marginal even at high values of pressure and non-equilibrium parameter θ.
Chang, Shu-Chiuan; Shrock, Robert
2001-07-01
The q-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width Ly and arbitrary length Lx has the form Z(G,q,v)=∑ j=1N Z,G,λ c Z,G,j(λ Z,G,j) L x, where v is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ( v=-1) is the chromatic polynomial P( G, q). Using coloring and transfer matrix methods, we give general formulas for C X,G=∑ j=1N X,G,λ c X,G,j for X= Z, P on cyclic and Möbius strip graphs of the square and triangular lattice. Combining these with a general expression for the (unique) coefficient cZ, G, j of degree d in q: c (d)=U 2d( q/2) , where Un( x) is the Chebyshev polynomial of the second kind, we determine the number of λZ, G, j's with coefficient c( d) in Z( G, q, v) for these cyclic strips of width Ly to be n Z(L y,d)=(2d+1)(L y+d+1) -1{2L y}/{L y-d } for 0⩽ d⩽ Ly and zero otherwise. For both cyclic and Möbius strips of these lattices, the total number of distinct eigenvalues λZ, G, j is calculated to be N Z,L y,λ = {2L y}/{L y}. Results are also presented for the analogous numbers nP( Ly, d) and NP, Ly, λ for P( G, q). We find that nP( Ly,0)= nP( Ly-1,1)= MLy-1 (Motzkin number), nZ( Ly,0)= CLy (the Catalan number), and give an exact expression for NP, Ly, λ. Our results for NZ, Ly, λ and NP, Ly, λ apply for both the cyclic and Möbius strips of both the square and triangular lattices; we also point out the interesting relations NZ, Ly, λ=2 NDA, tri, Ly and NP, Ly, λ=2 NDA, sq, Ly, where NDA, Λ, n denotes the number of directed lattice animals on the lattice Λ. We find the asymptotic growths NZ, Ly, λ∼ Ly-1/24 Ly and NP, Ly, λ∼ Ly-1/23 Ly as Ly→∞. Some general geometric identities for Potts model partition functions are also presented.
Roghanian, Ali; Sallenave, Jean-Michel
2008-03-01
Proteases and antiproteases have multiple important roles both in normal homeostasis and during inflammation. Antiprotease molecules may have developed in a parallel network, consisting of "alarm" and "systemic" inhibitors. Their primary function was thought until recently to mainly prevent the potential injurious effects of excess release of proteolytic enzymes, such as neutrophil elastase (NE), from inflammatory cells. However, recently, new potential roles have been ascribed to these antiproteases. We will review "canonical" and new "noncanonical" functions for these molecules, and more particularly, those pertaining to their role in innate and adaptive immunity (antibacterial activity and biasing of the adaptive immune response). PMID:18518838
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H−, H2+, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities
Turkheimer, Federico E; Leech, Robert; Expert, Paul; Lord, Louis-David; Vernon, Anthony C
2015-08-01
A variety of anatomical and physiological evidence suggests that the brain performs computations using motifs that are repeated across species, brain areas, and modalities. The computational architecture of cortex, for example, is very similar from one area to another and the types, arrangements, and connections of cortical neurons are highly stereotyped. This supports the idea that each cortical area conducts calculations using similarly structured neuronal modules: what we term canonical computational motifs. In addition, the remarkable self-similarity of the brain observables at the micro-, meso- and macro-scale further suggests that these motifs are repeated at increasing spatial and temporal scales supporting brain activity from primary motor and sensory processing to higher-level behaviour and cognition. Here, we briefly review the biological bases of canonical brain circuits and the role of inhibitory interneurons in these computational elements. We then elucidate how canonical computational motifs can be repeated across spatial and temporal scales to build a multiplexing information system able to encode and transmit information of increasing complexity. We point to the similarities between the patterns of activation observed in primary sensory cortices by use of electrophysiology and those observed in large scale networks measured with fMRI. We then employ the canonical model of brain function to unify seemingly disparate evidence on the pathophysiology of schizophrenia in a single explanatory framework. We hypothesise that such a framework may also be extended to cover multiple brain disorders which are grounded in dysfunction of GABA interneurons and/or these computational motifs. PMID:25956253
Molecular orbital estimation of reduced partition function ratios of small water clusters
Structures of water clusters, (H2O)n, up to n=10 were optimized at the HF/6-31G(d) level of theory, and H/D and 16O/18O isotopic reduced partition function ratios (RPFRs) at the optimized structures were calculated. The H/D RPFR values were distinctly different between hydrogen-bonded hydrogen atoms and non-hydrogen-bonded hydrogen atoms, but were nearly independent of the cluster size for n equal to 3 or larger when only the lowest-energy conformers are taken into consideration. The 16O/18O RPFR values were also distinct between hydrogen-bonded oxygen atoms and non-hydrogen-bonded oxygen atoms, but little difference in RPFR value was observed between oxygen atoms with one hydrogen bond and those with two hydrogen bonds. The 16O/18O RPFR values were cluster size independent above n=6. The estimation of RPFRs of liquid water thus seemed possible by considering the lowest energy conformers of small water clusters (n=6-10). (author)
Canonical density matrix perturbation theory.
Niklasson, Anders M N; Cawkwell, M J; Rubensson, Emanuel H; Rudberg, Elias
2015-12-01
Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures. PMID:26764847
Abroi, Aare; Ilves, Ivar; Kivi, Sirje; Ustav, Mart
2004-01-01
Recent studies have suggested that the tethering of viral genomes to host cell chromosomes could provide one of the ways to achieve their nuclear retention and partitioning during extrachromosomal maintenance in dividing cells. The data we present here provide firm evidence that the partitioning of the bovine papillomavirus type 1 (BPV1) genome is dependent on the chromatin attachment process mediated by viral E2 protein and its multiple binding sites. On the other hand, the attachment of E2 ...
Kallen, Johan; Zabzine, Maxim
2012-01-01
Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of r/g^2, where g is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.
Mielke, Steven L; Truhlar, Donald G
2016-01-21
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function. PMID:26801023
Mielke, Steven L.; Truhlar, Donald G.
2016-01-01
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
Constrained Canonical Correlation.
DeSarbo, Wayne S.; And Others
1982-01-01
A variety of problems associated with the interpretation of traditional canonical correlation are discussed. A response surface approach is developed which allows for investigation of changes in the coefficients while maintaining an optimum canonical correlation value. Also, a discrete or constrained canonical correlation method is presented. (JKS)
An algorithm to approximately calculate the partition function (and subsequently ensemble averages) and density of states of lattice spin systems through non-Monte-Carlo random sampling is developed. This algorithm (called the sampling-the-mean algorithm) can be applied to models where the up or down spins at lattice nodes interact to change the spin states of other lattice nodes, especially non-Ising-like models with long-range interactions such as the biological model considered here. Because it is based on the Central Limit Theorem of probability, the sampling-the-mean algorithm also gives estimates of the error in the partition function, ensemble averages, and density of states. Easily implemented parallelization strategies and error minimizing sampling strategies are discussed. The sampling-the-mean method works especially well for relatively small systems, systems with a density of energy states that contains sharp spikes or oscillations, or systems with little a priori knowledge of the density of states
Potts model partition functions for self-dual families of strip graphs
Chang, Shu-Chiuan; Shrock, Robert
2001-12-01
We consider the q-state Potts model on families of self-dual strip graphs GD of the square lattice of width Ly and arbitrarily great length Lx, with periodic longitudinal boundary conditions. The general partition function Z and the T=0 antiferromagnetic special case P (chromatic polynomial) have the respective forms ∑ j=1 NF, Ly, λcF, Ly, j( λF, Ly, j) Lx, with F= Z, P. For arbitrary Ly, we determine (i) the general coefficient cF, Ly, j in terms of Chebyshev polynomials, (ii) the number nF( Ly, d) of terms with each type of coefficient, and (iii) the total number of terms NF, Ly, λ. We point out interesting connections between the nZ( Ly, d) and Temperley-Lieb algebras, and between the NF, Ly, λ and enumerations of directed lattice animals. Exact calculations of P are presented for 2⩽ Ly⩽4. In the limit of infinite length, we calculate the ground state degeneracy per site (exponent of the ground state entropy), W( q). Generalizing q from Z+ to C, we determine the continuous locus B in the complex q plane where W( q) is singular. We find the interesting result that for all Ly values considered, the maximal point at which B crosses the real q-axis, denoted qc, is the same, and is equal to the value for the infinite square lattice, qc=3. This is the first family of strip graphs of which we are aware that exhibits this type of universality of qc.
Experimental Energy Levels and Partition Function of the 12C2 Molecule
Furtenbacher, Tibor; Szabó, István; Császár, Attila G.; Bernath, Peter F.; Yurchenko, Sergei N.; Tennyson, Jonathan
2016-06-01
The carbon dimer, the 12C2 molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for 12C2, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5699 rovibronic energy levels, 1325, 4309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the {{a}}{}3{{{\\Pi }}}{{u}} state, corresponding to the J = 2 total angular momentum quantum number and the F 1 spin-multiplet component, is 603.817(5) cm‑1. This well-determined energy difference should facilitate observations of singlet–triplet intercombination lines, which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with ab initio variational ones based on empirically adjusted and spin–orbit coupled potential energy curves obtained using the Duo code, are used to obtain a highly accurate partition function, and related thermodynamic data, for 12C2 up to 4000 K.
Multiplicity fluctuations in heavy-ion collisions using canonical and grand-canonical ensemble
Garg, P. [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Science, Simrol (India); Mishra, D.K.; Netrakanti, P.K.; Mohanty, A.K. [Bhabha Atomic Research Center, Nuclear Physics Division, Mumbai (India)
2016-02-15
We report the higher-order cumulants and their ratios for baryon, charge and strangeness multiplicity in canonical and grand-canonical ensembles in ideal thermal model including all the resonances. When the number of conserved quanta is small, an explicit treatment of these conserved charges is required, which leads to a canonical description of the system and the fluctuations are significantly different from the grand-canonical ensemble. Cumulant ratios of total-charge and net-charge multiplicity as a function of collision energies are also compared in grand-canonical ensemble. (orig.)
Multiplicity fluctuations in heavy ion collisions using canonical and grand canonical ensemble
Garg, P; Netrakanti, P K; Mohanty, A K
2015-01-01
We report the higher order cumulants and their ratios for baryon, charge and strangeness multiplicity in canonical and grand-canonical ensembles in ideal thermal model including all the resonances. When the number of conserved quanta is small, an explicit treatment of these conserved charges is required, which leads to a canonical description of the system and the fluctuations are significantly different from the grand canonical ensemble. Cumulant ratios of total charge and net-charge multiplicity as a function of collision energies are also compared in grand canonical ensemble.