Simple Algebraic Rules Research Articles

Accurate and Efficient Simulation Models for Power Electronics Transformers Based on Series-Connected Active Unity Power Factor Rectifier Modules

This paper contributes an efficient simulation technique for input-series output-parallel multilevel power electronics transformers based on active unity-power-factor rectifiers as building blocks. The technical motivation of the work comes from the fact that the computational burden for the simulation of these technologies tends to become unaffordable as the number of modules grows when using commercial software blocksets. This paper presents a new method to drastically reduce the simulation complexity by simplifying the switching rules: in a three-phase circuit, each phase zero-crossing condition is implemented by a single and simple algebraic rule, so the complex calculations for determining the conduction state of each single diode are removed from the model. The computational enhancement and accuracy of the proposed technique are proved by experimental verification using a single-phase single-cell prototype together with multiple simulations of full-scale systems of different sizes.

Topological Metadefects: Tangles of Dislocations.

The concept of topological defects is universal. In condensed matter, it applies to disclinations, dislocations, or vortices that are fingerprints of symmetry breaking during phase transitions. Using as a generic example the tangles of dislocations, we introduce the concept of topological metadefects, i.e., defects made of defects. We show that in cholesterics, dextrogyre and levogyre primary tangles are generated through the D_{2}→C_{2} symmetry breaking from the coplanar dislocation pair called Lehmann cluster submitted to a high enough tensile strain. The primary tangles can be wound up individually into double helices. They can also annihilate in pairs or associate into tangles of higher orders following simple algebraic rules.

A differential representation of cosmological wavefunctions

Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological spacetimes. While scattering amplitudes in flat space at tree level are obtained from simple algebraic operations, things are harder for cosmological observables. Indeed, computing cosmological correlation functions or the associated wavefunction coefficients requires evaluating a growing number of nested time integrals already at tree level, which is computationally challenging. Here, we present a new “differential” representation of the perturbative cosmological wavefunction in de Sitter spacetime that obviates this problem for a large class of phenomenologically relevant theories. Given any tree-level Feynman-Witten diagram, we give simple algebraic rules to write down a seed function and a differential operator that transforms it into the desired wavefunction coefficient for any scale-invariant, parity-invariant theory of massless scalars and gravitons with general boost-breaking interactions. In particular, this applies to large classes of phenomenologically relevant theories such as those described by the effective field theory of inflation or solid inflation. Trading nested bulk time integrals for derivatives on boundary kinematical data provides a great computational advantage, especially for processes involving many vertices.

Exact Semianalytical Calculation of Rotation Curves with Bekenstein–Milgrom Nonrelativistic MOND

Abstract Astronomers derive MOdified Newtonian Dynamics (MOND) rotation curves using the simple algebraic rule of calculating the acceleration as equal to the Newtonian acceleration (a) divided by some factor μ(a). However, there are velocity differences between this simple rule and the calculation derived from more sophisticated MOND versions such as AQUAL or QMOND, created to expand MOND heuristic law and preserve the conservation of momentum, angular momentum, and energy, and follow the weak equivalence principle. Here we provide recipes based on Milgrom’s proposal to calculate semianalytically (without numerical simulations) MOND rotation curves for any density distribution based on AQUAL, applying it to different models of thin disks. The application of this formalism is equivalent to the creation of a fictitious phantom mass whose field may be used in a Newtonian way to calculate iteratively the MOND accelerations. In most cases, the differences between the application of the simple algebraic rule and the AQUAL-MOND calculations are small, ≲5%. However, the error of the algebraic solution is larger than 5% when more than half of the mass is in the MONDian regime (where Newtonian and MOND rotation speeds differ by more than 10%), reaching in some cases >70% discrepancy, such as in Maclaurin disks, representative of galaxies for which the rotational velocity rises to the edge of the disk as is seen in irregular galaxies. The slope of the rotation speed in the dependence with the radius or the vertical distance of the plane is also significantly changed.

Fast value iteration: an application of Legendre-Fenchel duality to a class of deterministic dynamic programming problems in discrete time

ABSTRACTWe propose an algorithm, which we call ‘Fast Value Iteration’ (FVI), to compute the value function of a deterministic infinite-horizon dynamic programming problem in discrete time. FVI is an efficient algorithm applicable to a class of multidimensional dynamic programming problems with concave return (or convex cost) functions and linear constraints. In this algorithm, a sequence of functions is generated starting from the zero function by repeatedly applying a simple algebraic rule involving the Legendre-Fenchel transform of the return function. The resulting sequence is guaranteed to converge, and the Legendre-Fenchel transform of the limiting function coincides with the value function.

Phonological Concept Learning.

Linguistic and non-linguistic pattern learning have been studied separately, but we argue for a comparative approach. Analogous inductive problems arise in phonological and visual pattern learning. Evidence from three experiments shows that human learners can solve them in analogous ways, and that human performance in both cases can be captured by the same models. We test GMECCS (Gradual Maximum Entropy with a Conjunctive Constraint Schema), an implementation of the Configural Cue Model (Gluck & Bower, ) in a Maximum Entropy phonotactic-learning framework (Goldwater & Johnson, ; Hayes & Wilson, ) with a single free parameter, against the alternative hypothesis that learners seek featurally simple algebraic rules ("rule-seeking"). We study the full typology of patterns introduced by Shepard, Hovland, and Jenkins () ("SHJ"), instantiated as both phonotactic patterns and visual analogs, using unsupervised training. Unlike SHJ, Experiments 1 and 2 found that both phonotactic and visual patterns that depended on fewer features could be more difficult than those that depended on more features, as predicted by GMECCS but not by rule-seeking. GMECCS also correctly predicted performance differences between stimulus subclasses within each pattern. A third experiment tried supervised training (which can facilitate rule-seeking in visual learning) to elicit simple rule-seeking phonotactic learning, but cue-based behavior persisted. We conclude that similar cue-based cognitive processes are available for phonological and visual concept learning, and hence that studying either kind of learning can lead to significant insights about the other.

Observability and reachability of simple grid and torus graphs

AbstractIn this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid or a torus. More in detail, under suitable conditions on the eigenvalue multiplicity, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is observable (reachable). For any set of observation (leader) nodes, we provide a closed form expression for the unobservable (unreachable) eigenvalues and for the eigenvectors of the unobservable (unreachable) subsystem.

Synthesis and Dynamic Switching of Surface Plasmon Vortices with Plasmonic Vortex Lens

The generation of surface plasmon vortices with arbitrary higher order vortex topological charges with novel plasmonic vortex lens is experimentally demonstrated. It is shown that the polarization sensitivity of the plasmonic vortex lens can be utilized for the dynamic switching of the surface plasmon vortices with different topological charges. A simple algebraic rule related to the vortex topological charge change in the dynamic switching is formulated, and its proof is provided with theory and experiment. The synthesis and dynamic switching of higher order surface plasmon vortices have profound potential in optical trapping, optical data storage, and other related fields.

Infant Rule Learning Facilitated by Speech

Sequences of speech sounds play a central role in human cognitive life, and the principles that govern such sequences are crucial in determining the syntax and semantics of natural languages. Infants are capable of extracting both simple transitional probabilities and simple algebraic rules from sequences of speech, as demonstrated by studies using ABB grammars (la ta ta, gai mu mu, etc.). Here, we report a striking finding: Infants are better able to extract rules from sequences of nonspeech--such as sequences of musical tones, animal sounds, or varying timbres--if they first hear those rules instantiated in sequences of speech.

Cognitive Algebra in Sport Decision-Making

Two studies examined whether simple algebraic rules that have been shown to be operative in many applied settings may also be found in sport decision-making. The theoretical framework for these studies was the Functional Theory of Cognition (Anderson, Contributions to information integration theory. Hillsdale, NJ: Erlbaum, 1996). The way in which novices but already experienced team sport players (soccer, basketball, and handball players) combine different informational cues (relative importance of the game, numerical status of the team, current score, and time left to play) for deciding a quick restart of play near the end of a match was examined. The basic finding are consistent with the proposition that the knowledge bases at work for judging the appropriateness of this type of sport decisions are structured according to simple algebraic rules.

Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear, non-linear, and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ρ = γ f(ρ). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p φ+ρφ = γρφ β are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.

A new efficient approach to the direct restricted active space self-consistent field method

We present an implicitly parallel method for integral-block driven restricted active space self-consistent field (RASSCF) algorithms. Our algorithm entirely avoids testing the index space for nonzero contributions to the CI vector, by finding entire blocks of contributions through use of simple algebraic rules (propagation rules). The blocks themselves are efficiently identified by introducing a RAS model space. Our algorithm is capable of making efficient use of modern supercomputer hardware, supporting both shared and distributed memory architectures and hybrids. Applicability of our method is demonstrated with a RASSCF investigation of the first two excited states of indole.

Circuit Applications of ‘Dunn's Rule’

A simple algebraic rule can often be used as an alternative to the application of differential calculus when seeking or demonstrating the occurrence of maximum or minimum conditions in a circuit or system (e.g. the conditions for maximum power transfer). Teaching experience has proved the rule to be especially effective and convenient when teaching introductory electronics courses to technician students.

Exact solution of a 1D asymmetric exclusion model using a matrix formulation

Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be solved exactly in the case of open boundaries. Here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices. With this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules. They obtain several explicit forms for these non-commuting matrices which are, in the general case, infinite-dimensional. Their approach allows exact expressions to be derived for the current and density profiles. Finally they discuss briefly two possible generalizations of their results: the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles.

Inherent limitations in the effective-beam technique for algorithmic solutions to radiative corrections

The algebraic structure of the amplitude describing the process e +e − → V + γ, V + γγ is studied, where V stands for a (possibly off-shell) photon or Z boson which can decay into any final state. A simple algebraic rule is given for determining whether such an amplitude can be expressed in terms of the lowest-order, nonradiative amplitude multiplied by factors that take into account the emission of the bremsstrahlung photons. This rule is shown to be satisfied for all single-bremsstrahlung helicity amplitudes but not for some of the double-bremsstrahlung helicity amplitudes. It follows that there are structure-function based algorithms which give the exact result for all possible distributions in single-photon bremsstrahlung, but that no such algorithms are possible for double-photon bremsstrahlung. A few current implementations of these ideas in existing Monte Carlo programs are studied and found to be defective: a numerical study is presented which indicates the magnitude of the deviations from exactness in the single-photon bremsstrahlung case. An argument is given for the physics reasons behind the formal result in this paper. The accuracy of approaches that rely on structure functions for more than one bremsstrahlung photon is discussed. It is shown that the ultimate accuracy possible when one restricts oneself to purely effective-beam techniques cannot be better than next-to-leading log, even if a K factor good to all orders is included.

Integration of semantic and structural constraints in narrative comprehension

The original debate between semantic and syntactic approaches to issues in reading comprehension has lost some of its appeal as psycholinguistics has embraced various interactive models of reading comprehension. This study, based on Information Integration Theory (Anderson, 1981, 1982) and its methodological counterpart, Functional Measurement, investigates whether semantic and structural information may be integrated during the comprehension process by means of a simple algebraic rule and whether the comprehension task may introduce a systematic bias to this process. Twelve high school students participated in a series of experiments which attempted to cross‐validate the basic findings. Subjects were asked metalinguistic questions dealing with the logic and organizational nature of the story to be comprehended. The logic of the story was manipulated by varying the relative compatibility of an industrious protagonist and his report of having done ‘all/some/none’ of the work assigned to him. The structural...

Quantum theory of magnetic electron lenses based on the Dirac equation

A quantum theory of magnetic electron lenses based on a convenient formulation of the Dirac theory is outlined. It is shown that the passage from the conventional scalar theory to the spinor theory can be accomplished through a simple algebraic rule in analogy with the passage from scalar to vector light optics.

Thinking about nothing: Development of concepts of zero

Two studies are reported investigating children's conceptions of the number zero. The first, with 31/2–61/2‐year‐olds, charts preschoolers' understanding that zero is a number among other numbers with its own unique value, namely nothing. Children's achievement of this understanding occurred in three phases. At each phase understanding of zero lagged behind comparable understanding of other small numbers. The second study, with 51/2–10‐year‐olds, investigated children's developing conception of simple algebraic rules, such as a + 0 = a. Results showed that even the younger children had some understanding of several algebraic rules. The older children had acquired more such knowledge, but at all ages algebraic understanding was advanced for rules pertaining to zero, in comparison to those pertaining to other small numbers. These results suggest that zero plays a special role in children's increasingly algebraic knowledge of number. We conclude that since zero is difficult to conceive of and use originally (Expt 1) children develop special rules for its use, and that this provides a first step towards their formulation of more general algebraic rules (Expt 2) and towards an expanded conception of number and mathematics.

THE PROBABLE SEQUENCE OF NUCLEOTIDES IN SOME CODONS.

Proposals arranging the order of nucleotides in the triplets which code for amlino acidsl'-3 have heretofore depended solely upon amino acid replacement data, excepting only the tenuous proposal that AUU and GUU may be the ordered codons for tyrosine and cysteine, respectively. It is obvious, however, that even if we had knowledge of all possible amino acid replacements, we could still write down six internally consistent sets of codons, each set being convertible to another set by some simple algebraic rule (e.g., reverse the order of nucleotides in all codons, or interchange all first nucleotides with the second). The final solution to the order of nucleotides in the codons will undoubtedly have to await the chemical synthesis of ordered polynucleotides, but the work of Gatlin and Davis4 indicates that another means may be available to determine the nucleotide order for some codons. They observed in a group of four organisms that as the lysine content increased, so also did the frequency of doublet nucleotides containing A and T. This result is consistent with the known codon composition of lysine. They did not possess sufficient data to go beyond this conclusion, but it is apparent that if sufficient data were at hand, one might actually be able to correlate the specifically ordered nucleotide doublets with specific amino acids. The chief reservation results from the many potential sources of noise in the system, and one cannot be sure beforehand that one can discriminate the looked-for effect from that noise. On the assumption that one could, however, data were collected on the total protein composition of several organisms for which the doublet nucleotide frequency had already been determined by Josse et al.' and Swartz et al.6 The correspondence between the two parameters was tested for statistical significance, and 26 associations between ordered doublets and specific amino acids were found which were positively correlated at a 95 per cent or better level of confidence.