Alternative Formalism Research Articles

How to Model Mechanistic Hierarchies

Mechanisms are usually viewed as hierarchical, with lower levels of a mechanism influencing, and decomposing, its higher-level behavior. To draw quantitative predictions from a model of a mechanism, the model must capture this hierarchical aspect. Recursive Bayesian networks (RBNs) were put forward by Lorenzo Casini et al. as a means to model mechanistic hierarchies by decomposing variables into their constituting causal networks. The proposal was criticized by Alexander Gebharter. He proposes an alternative formalism, which instead decomposes arrows. Here, I defend RBNs from the criticism and argue that they offer a better representation of mechanistic hierarchies than the rival account.

On the Napsuciale-Kirchbach Formalism for Spin 3/2 Field Theory

We consider the newly approach by Napsuciale and Kirchbach as an alternative formalism for spin-3/2 fields. The Feynman rules for interacting case are derived. Gauge invariance property in this formalism is shown from the corresponding invariant Compton scattering amplitude related to gauge transformation of the polarization vector.

Set-theoretic types for polymorphic variants

Polymorphic variants are a useful feature of the OCaml language whose current definition and implementation rely on kinding constraints to simulate a subtyping relation via unification. This yields an awkward formalization and results in a type system whose behaviour is in some cases unintuitive and/or unduly restrictive. In this work, we present an alternative formalization of polymorphic variants, based on set-theoretic types and subtyping, that yields a cleaner and more streamlined system. Our formalization is more expressive than the current one (it types more programs while preserving type safety), it can internalize some meta-theoretic properties, and it removes some pathological cases of the current implementation resulting in a more intuitive and, thus, predictable type system. More generally, this work shows how to add full-fledged union types to functional languages of the ML family that usually rely on the Hindley-Milner type system. As an aside, our system also improves the theory of semantic subtyping, notably by proving completeness for the type reconstruction algorithm.

Alternative self-dual gravity in eight dimensions

We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell–Mansouri physical framework and a self-dual curvature symmetry, we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein–Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions.

Investigation of the problems of the allocation of resources among enterprises

The problem of the allocation of resources among enterprises from different industries as parts of the economic conglomerate is considered. The different ways of stating the problem and inputting the data, taking into account the possibility of building their own functions of return, control action, and time are presented. The key method of solving the problem is the dynamic programming [1]. Also, we investigated an alternative formalization of the problem in which the phase and control variables may take an infinite number of values, which made it impossible to use standard tables for dynamic programming and lead to analytical calculations. In the latter case, we provide a number of limitations, which convert the function of return to the form that satisfies the conditions of production functions.

Pure Logic of Many-Many Ground

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta (2014). In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground (plg) can be extended to the many-many case, giving rise to the Pure Logic of Many-Many Ground (plmmg). In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete.

Dynamical system analysis for a nonminimal torsion-matter coupled gravity

In this work, we perform a detailed dynamical analysis for the cosmological applications of a nonminimal torsion-matter coupled gravity. Two alternative formalisms are proposed, which enable one to choose between the easier approach for a given problem, and furthermore, we analyze six specific models. In general, we extract fixed points corresponding either to dark-matter dominated, scaling decelerated solutions, or to dark-energy dominated accelerated solutions. Additionally, we find that there is a small parameter region in which the model can experience the transition from the matter epoch to a dark-energy era. These features are in agreement with the observed universe evolution, and make the theory a successful candidate for the description of Nature.

A Constraint Approach to Pivot-Based Bilingual Dictionary Induction

High-quality bilingual dictionaries are very useful, but such resources are rarely available for lower-density language pairs, especially for those that are closely related. Using a third language to link two other languages is a well-known solution and usually requires only two input bilingual dictionaries A-B and B-C to automatically induce the new one, A-C . This approach, however, has never been demonstrated to utilize the complete structures of the input bilingual dictionaries, and this is a key failing because the dropped meanings negatively influence the result. This article proposes a constraint approach to pivot-based dictionary induction where language A and C are closely related. We create constraints from language similarity and model the structures of the input dictionaries as a Boolean optimization problem, which is then formulated within the Weighted Partial Max-SAT framework, an extension of Boolean Satisfiability (SAT). All of the encoded CNF (Conjunctive Normal Form), the predominant input language of modern SAT/MAX-SAT solvers, formulas are evaluated by a solver to produce the target (output) bilingual dictionary. Moreover, we discuss alternative formalizations as a comparison study. We designed a tool that uses the Sat4j library as the default solver to implement our method and conducted an experiment in which the output bilingual dictionary achieved better quality than the baseline method.

Distributions of a Linear Homopolymer Additive in an Ordered Block Copolymer Matrix As Quantified by Small-Angle Neutron Scattering

The addition of linear poly(acrylic acid) (PAA) to a disordered low molecular mass poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) triblock copolymer host (PEO-b-PPO-b-PEO) is known to induce an ordering transition. Small-angle neutron scattering (SANS) measurements are presented to quantify the spatial distribution of the linear homopolymer additive within the ordered microstructure by using deuterium-labeled block copolymers. The analysis, however, requires revisiting the conventional algorithm of expressing the scattering intensity as a product of a form and structure factor, where the two terms are independent, and an alternate formalism is introduced that couples these terms. The SANS data are consistent with a lamellar morphology, but with the unusual caveat of a weak first-order scattering peak relative to a strong second-order peak. This necessitates the use of a four-layer structure for the lamellar repeat unit where the center of the PEO domain is enriched with PAA. The SANS data are fit to quantify the compositional profiles of the three components across the four-layer lamellar repeat unit. As the concentration and/or molecular mass of the PAA additive increases, PEO–PAA-rich and PPO-rich domains gradually emerge. However, it is not until relatively high PAA loadings that compositionally pure PPO domains appear. While the PAA additive is known to form hydrogen bonds with the PEO segments, the measurements suggest that the unfavorable interactions between the PAA and PPO are also important for driving the self-assembly process.

SU(4) harmonic superspace and supersymmetric gauge theory

We consider the harmonic-superspace formalism in the $N=4$ supersymmetry using the $SU(4)/SU(2)\times SU(2)\times U(1)$ harmonics which was earlier applied to the abelian gauge theory. The N=4 non-abelian constraints in a standard superspace are reformulated as the harmonic-superspace equations for two basic analytic superfields: the independent superfield strength W of a dimension 1 and the dimensionless harmonic gauge 4-prepotential V having the $U(1)$ charge 2. These constraint equations I manifestly depend on the Grassmann coordinates $\theta$, although they are covariant under the unusual N=4 supersymmetry transformations. We analyze an alternative harmonic formalism of the supergauge theory for two unconstrained nonabelian analytic superfields W and V. The gauge-invariant action A(W,V) in this formalism contains $\theta$ factors in each term, it is invariant under the $SU(4)$ automorphism group. In this model, the interaction of two infinite-dimensional N=4 supermultiplets with the physical and auxiliary fields arises at the level of component fields. The action A(W,V) generate analytic equations of motion II alternative to the harmonic-superspace superfield constraints I. Both sets of equations give us the equivalent equations for the physical component fields of the $N=4$ gauge supermultiplet, they connect auxiliary and physical fields of two superfields. The nonlinear effective interaction of the abelian harmonic superfield W is constructed.

Variational method with staggered fermions

The variational method is used widely for determining eigenstates of the QCD hamiltonian for actions with a conventional transfer matrix, e.g., actions with improved Wilson fermions. An alternative lattice fermion formalism, staggered fermions, does not have a conventional single-time-step transfer matrix. Nonetheless, with a simple modification, the variational method can also be applied to that formalism. In some cases the method also provides a mechanism for separating the commonly paired parity-partner states. We discuss the extension to staggered fermions and illustrate it by applying it to the calculation of the spectrum of charmed-antistrange mesons consisting of a clover charm quark and a staggered strange antiquark.

Breaking conceptual locks in modelling root absorption of nutrients: reopening the thermodynamic viewpoint of ion transport across the root.

The top-down analysis of nitrate influx isotherms through the Enzyme-Substrate interpretation has not withstood recent molecular and histochemical analyses of nitrate transporters. Indeed, at least four families of nitrate transporters operating at both high and/or low external nitrate concentrations, and which are located in series and/or parallel in the different cellular layers of the mature root, are involved in nitrate uptake. Accordingly, the top-down analysis of the root catalytic structure for ion transport from the Enzyme-Substrate interpretation of nitrate influx isotherms is inadequate. Moreover, the use of the Enzyme-Substrate velocity equation as a single reference in agronomic models is not suitable in its formalism to account for variations in N uptake under fluctuating environmental conditions. Therefore, a conceptual paradigm shift is required to improve the mechanistic modelling of N uptake in agronomic models. An alternative formalism, the Flow-Force theory, was proposed in the 1970s to describe ion isotherms based upon biophysical 'flows and forces' relationships of non-equilibrium thermodynamics. This interpretation describes, with macroscopic parameters, the patterns of N uptake provided by a biological system such as roots. In contrast to the Enzyme-Substrate interpretation, this approach does not claim to represent molecular characteristics. Here it is shown that it is possible to combine the Flow-Force formalism with polynomial responses of nitrate influx rate induced by climatic and in planta factors in relation to nitrate availability. Application of the Flow-Force formalism allows nitrate uptake to be modelled in a more realistic manner, and allows scaling-up in time and space of the regulation of nitrate uptake across the plant growth cycle.

Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator

The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl. Phys. B 885 (2014) 150] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton-Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory) is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

A conditional logic for abduction

We propose a logic of abduction that (i) provides an appropriate formalization of the explanatory conditional, and that (ii) captures the defeasible nature of abductive inference. For (i), we argue that explanatory conditionals are non-classical, and rely on Brian Chellas’s work on conditional logics for providing an alternative formalization of the explanatory conditional. For (ii), we make use of the adaptive logics framework for modeling defeasible reasoning. We show how our proposal allows for a more natural reading of explanatory relations, and how it overcomes problems faced by other systems in the literature.

How (not) to teach Lorentz covariance of the Dirac equation

In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional non-standard bilinear combinations with well-defined transformation properties.

Four-dimensional Rotations in Coherent Optical Communications

To model electromagnetic wave propagation for coherent communications without polarization dependent losses, the unitary 2 ×2 Jones transfer matrix formalism is typically used. In this study, we propose an alternative formalism to describe such transformations based on rotations in four-dimensional (4d) Euclidean space. This formalism is usually more attractive from a communication theoretical perspective, since decisions and symbol errors can be related to geometric concepts such as Euclidean distances between points and decision boundaries. Since 4d rotations is a richer description than the conventional Jones calculus, having six rather than four degrees of freedom (DOF), we propose an extension of the Jones calculus to handle all six DOF. In addition, we show that the two extra DOF in the 4d description represents transformations that are nonphysical for propagating photons, since they does not obey the fundamental quantum mechanical boson commutation relations. Finally, we exemplify on how the nonphysical rotations can change the polarization-phase degeneracy of well-known constellations such as single-polarization QPSK, polarization-multiplexed (PM-)QPSK and polarization-switched (PS-) QPSK. For example, we show how PM-QPSK, which is well known to consist of four polarization states each having four-fold phase degeneracy, can be represented as eight states of polarizations, each with binary phase degeneracy.

Interacting and fractional topological insulators via theZ2chiral anomaly

Recently it was shown that the topological properties of $2D$ and $3D$ topological insulators are captured by a $\mathbb{Z}_2$ chiral anomaly in the boundary field theory. It remained, however, unclear whether the anomaly survives electron-electron interactions. We show that this is indeed the case, thereby providing an alternative formalism for treating topological insulators in the interacting regime. We apply this formalism to fractional topological insulators (FTI) via projective/parton constructions and use it to test the robustness of all fractional topological insulators which can be described in this way. The stability criterion we develop is easy to check and based on the pairswitching behaviour of the noninteracting partons. In particular, we find that FTIs based on bosonic Laughlin states and the $M=0$ bosonic Read-Rezayi states are fragile and may have a completely gapped and non-degenerate edge spectrum in each topological sector. In contrast, the $\mathbb{Z}_{k}$ Read-Rezayi states with $M=1$ and odd $k$ and the bosonic $3D$ topological insulator with a $\pi/4$ fractional theta-term are topologically stable.

Some remarks on metric and deformation

This work is aimed at emphasising the relationship between metric and deformation, under the light of a novel formalism for the Polar Decomposition Theorem. All results are first presented in the classical formalism of Cauchy’s celebrated theorem, and then in the proposed alternative formalism. Although the latter requires a little more work to be established, it allows for directly defining all strain tensors as “covariant”, i.e. with both feet being covectors. Emphasis is also placed on how, in the absence of the metric structure, the available mathematical tools are restricted to the deformation gradient alone. Along with these main results, and in the didactical intention that permeates this work, several hints are given, which could be useful in teaching Continuum Mechanics, e.g. the rigorous definition of the determinant of the deformation gradient in Riemannian manifolds, and a caveat on the definition of the spatial Hencky logarithmic strain. The setting is that of modern Continuum Mechanics, based on the description given by Differential Geometry in terms of differentiable manifolds. However, passing to the simpler case of affine spaces takes almost no effort, paying attention to keeping the distinction between vectors and covectors, and therefore allowing the matrices representing the metric tensors to differ from the unit matrix.

Erratum: Phenomenology of QCD threshold resummation for gluino pair production at NNLL

We examine the impact of threshold resummation for the inclusive hadronic production cross section of gluino pairs at next-to-next-to-leading-logarithmic accuracy, compared to the exact next-to-leading-order cross section and the next-to-next-to-leading-order approximation. Here, we apply formulas derived recently in the classical Mellin-space formalism. Moreover, we give the analytic input for the alternative momentum-space formalism and discuss the crucial points of the numeric implementation. We find that soft resummation keeps the hadronic cross section close to the fixed next-to-leading-order result.

Charge screening by thin shells in a 2+1-dimensional regular black hole

We consider a particular Bardeen black hole in 2+1-dimensions. The black hole is sourced by a radial electric field in non-linear electrodynamics (NED). The solution is obtained anew by the alternative Hamiltonian formalism. For $r\rightarrow \infty $ it asymptotes to the charged BTZ black hole. It is shown that by inserting a charged, thin-shell (or ring) the charge of the regular black hole can be screened from the external world.