Odd Loops Research Articles

Shedding new light on the foundations of abstract argumentation: Modularization and weak admissibility

In his seminal 1995 paper, Dung laid the foundations of abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack loop, unless the loop is broken up by some argument attacking the loop from outside. Motivated by the fact that such arguments represent self-contradictory or paradoxical arguments, he asked for reasonable semantics which overcome the problem that such arguments may indeed invalidate any argument they attack.This paper provides a solution to this problem. More precisely, we introduce alternative foundations for abstract argumentation, namely weak admissibility and weak defense. After showing that these key concepts are compatible as in the classical case we introduce new versions of the classical Dung-style semantics including complete, preferred and grounded semantics. We provide a rigorous study of these new concepts including interrelationships as well as the relations to their Dung-style counterparts. We also conduct an analysis of the relationship of our concepts with similar concepts found in the literature. We show that weak admissibility, although defined in entirely different terms, is in fact equivalent to a notion of acceptability which was defined by Kakas and Mancarella yet never studied in depth.The new semantics presented here overcome the issue with self-defeating arguments, and they are semantically insensitive to syntactic deletions of self-attacking arguments, a special case of self-defeat.1

Revisiting the Foundations of Abstract Argumentation – Semantics Based on Weak Admissibility and Weak Defense

In his seminal 1995 paper, Dung paved the way for abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack loop, unless the loop is broken up by some argument attacking the loop from outside. Motivated by the fact that such arguments represent self-contradictory or paradoxical arguments, he asked for reasonable semantics which overcome the problem that such arguments may indeed invalidate any argument they attack. This paper tackles this problem from scratch. More precisely, instead of continuing to use previous concepts defined by Dung we provide new foundations for abstract argumentation, so-called weak admissibility and weak defense. After showing that these key concepts are compatible as in the classical case we introduce new versions of the classical Dung-style semantics including complete, preferred and grounded semantics. We provide a rigorous study of these new concepts including interrelationships as well as the relations to their Dung-style counterparts. The newly introduced semantics overcome the issue with self-defeating arguments, and they are semantically insensitive to syntactic deletions of self-attacking arguments, a special case of self-defeat.

Odd Loop Regions of XenA and XenB Enzymes Modulate Their Interaction with Nitro-explosives Compounds and Provide Structural Support for Their Regioselectivity.

The nitro-explosive compounds 2,4,6-trinitrotoluene, 2,4,6-trinitrophenol, and 1,2,3-trinitroglycerol are persistent environmental contaminants. The presence of different functional groups in these molecules represents a great challenge to enzymatic catalysis. The chemical variety of these three substrates is such that they do not bind and interact with catalytic residues within an enzyme with the same affinity. In this context, two Xenobiotic Reductase enzymes produced by the bacteria Pseudomonas putida can catalyze the reduction of these compounds with different affinities and regioselectivity. The structural bases that support this substrate promiscuity and catalytic preferences are unknown. Therefore, through molecular dynamics simulations and free energy calculations, we explored the structural properties driving the specific interactions of these enzymes with their substrates and cofactor. Models of Xenobiotic Reductase A and B enzymes in complex with 2,4,6-trinitrotoluene, 2,4,6-trinitrophenol, or 1,2,3-trinitroglycerol were built, and the ligand enzyme interaction was simulated by molecular dynamics. The structural analysis of the molecular dynamics simulations shows that loops 3, 5, 7, 9, 11, and 13 of Xenobiotic Reductase B, and loops 4, 5, 7, 11, 13, and 15 Xenobiotic Reductase A, are in contact with the ligands during the first stages of the molecular recognition. These loops are the most flexible regions for both enzymes; however, Xenobiotic Reductase B presents a greater range of movement and a higher number of residues interacting with the ligands. Finally, the distance between the cofactor and the different reactive groups in the substrate reflects the regioselectivity of the enzymes, and the free energy calculations are consistent with the substrate specificity of both enzymes studied. The simulation shows a stable interaction between the aromatic ring of the substrates and Xenobiotic Reductase B. In contrast, a less stable interaction with the different nitro groups of the aromatic ligands was observed. In the case of 1,2,3-trinitroglycerol, Xenobiotic Reductase B interacts more closely with the nitro groups of carbon 1 or 3, while Xenobiotic Reductase A is more selective by nitro groups of carbon 2. The obtained results suggest that the flexibility of the loops in Xenobiotic Reductase B and the presence of polar and aromatic residues present in loops 5 and 7 are fundamental to determine the affinity of the enzyme with the different substrates, and they also contribute to the proper orientation of the ligands that directs the catalytic reaction.

The Characterization of the Variational Minimizers for Spatial RestrictedN+1-Body Problems

We use Jacobi's necessary condition for the variational minimizer to study the periodic solution for spatial restrictedN+1-body problems with a zero mass on the vertical axis of the plane forNequal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric loop space must be a nonconstant periodic solution for any2≤N≤472; hence the zero mass must oscillate, so that it cannot be always in the same plane with the other bodies. This result contradicts with our intuition that the small mass should always be at the origin.

Wilson loops in superconformal Chern-Simons theory and fundamental strings in Anti-de Sitter supergravity dual

We study Wilson loop operators in three-dimensional, = 6 superconformal Chern-Simons theory dual to IIA superstring theory on AdS4 × 3. Novelty of Wilson loop operators in this theory is that, for a given contour, there are two linear combinations of Wilson loop transforming oppositely under time-reversal transformation. We show that one combination is holographically dual to IIA fundamental string, while orthogonal combination is set to zero. We gather supporting evidences from detailed comparative study of generalized time-reversal transformations in both D2-brane worldvolume and ABJM theories. We then classify supersymmetric Wilson loops and find at most 1/6 supersymmetry. We next study Wilson loop expectation value in planar perturbation theory. For circular Wilson loop, we find features remarkably parallel to circular Wilson loop in = 4 super Yang-Mills theory in four dimensions. First, all odd loop diagrams vanish identically and even loops contribute nontrivial contributions. Second, quantum corrected gauge and scalar propagators take the same form as those of = 4 super Yang-Mills theory. Combining these results, we propose that expectation value of circular Wilson loop is given by Wilson loop expectation value in pure Chern-Simons theory times zero-dimensional Gaussian matrix model whose variance is specified by an interpolating function of `t Hooft coupling. We suggest the function interpolates smoothly between weak and strong coupling regime, offering new test ground of the AdS/CFT correspondence.

Zero temperature solutions of the Edwards-Anderson model in random Husimi lattices

We solve the Edwards-Anderson model (EA) in different Husimi lattices using the cavity method at replica symmetric (RS) and 1-step of replica symmetry breaking (1RSB) levels. We show that, at T = 0, the structure of the solution space depends on the parity of the loop sizes. Husimi lattices with odd loop sizes may have a trivial paramagnetic solution thermodynamically relevant for highly frustrated systems while, in Husimi lattices with even loop sizes, this solution is absent. The range of stability under 1RSB perturbations of this and other RS solutions is computed analytically (when possible) or numerically. We also study the transition from 1RSB solutions to paramagnetic and ferromagnetic RS solutions. Finally we compare the solutions of the EA model in Husimi lattices with that on the (short loops free) Bethe lattices, showing that already for loop sizes of order 8 both models behave similarly.

Stable Surface-Wave Plasma through Excitation of Standing Surface Wave Using Plane Multislot Antenna

A stable high-density and low-temperature plasma was realized through excitation of standing surface waves using a plane multislot antenna. On a dielectric-window surface, the surface wave introduced from a slot interferes with that from the adjacent slot to generate a standing surface wave with odd loops at an interval of one-half wavelength of the surface wave between the slots. The plasma density is 2-10×1012 cm-3, thus the skin depth is 1.5–4 mm in the wide pressure range from 10 mTorr to 1 Torr. A superior high-density plasma with a relatively high temperature is generated near the dielectric window and a high-density plasma bulk with a low temperature is sustained through the intrinsic diffusion and the relaxation of the generated plasma. At high pressures of about 1 Torr, the plasma itself is confined near the dielectric window. The plasma is suitable for various applications, especially for high-rate and low-damage processes using large-area substrates.

The solution structure of reduced dimeric copper zinc superoxide dismutase. The structural effects of dimerization.

The solution structure of homodimeric Cu2Zn2 superoxide dismutase (SOD) of 306 aminoacids was determined on a 13C, 15N and 70% 2H labeled sample. Two-thousand eight-hundred and five meaningful NOEs were used, of which 96 intersubunit, and 115 dihedral angles provided a family of 30 conformers with an rmsd from the average of 0.78 +/- 0.11 and 1.15 +/- 0.09 A for the backbone and heavy atoms, respectively. When the rmsd is calculated for each subunit, the values drop to 0.65 +/- 0.09 and 1.08 +/- 0.11 A for the backbone and heavy atoms, respectively. The two subunits are identical on the NMR time scale, at variance with the X-ray structures that show structural differences between the two subunits as well as between different molecules in the unit cell. The elements of secondary structure, i.e. eight beta sheets, are the same as in the X-ray structures and are well defined. The odd loops (I, III and V) are well resolved as well as loop II located at the subunit interface. On the contrary, loops IV and VI show some disorder. The residues of the active cavity are well defined whereas within the various subunits of the X-ray structure some are disordered or display different orientation in different X-ray structure determinations. The copper(I) ion and its ligands are well defined. This structure thus represents a well defined model in solution relevant for structure-function analysis of the protein. The comparison between the solution structure of monomeric mutants and the present structure shows that the subunit-subunit interactions increase the order in loop II. This has the consequences of inducing the structural and dynamic properties that are optimal for the enzymatic function of the wild-type enzyme. The regions 37-43 and 89-95, constituting loops III and V and the initial part of the beta barrel and showing several mutations in familial amyotrophis lateral sclerosis (FALS)-related proteins have a quite extensive network of H-bonds that may account for their low mobility. Finally, the conformation of the key Arg143 residue is compared to that in the other dimeric and monomeric structures as well as in the recently reported structure of the CCS-superoxide dismutase (SOD) complex.

Bond graphs III: Bond graphs and electrical networks

Electrical networks are defined and a definition of when a bond graph and an electrical network are equivalent is given. Bond graphs and electrical networks are defined to be primitive if they contain no transformers or gyrators. A bond graph is defined to be realisable if it is equivalent to an electrical network and primitively realisable if it is equivalent to a primitive electrical network. It is shown how to construct a bond graph equivalent to a given electrical network and how to construct an electrical network equivalent to a given bond graph. Chordless odd loops are defined and a characterisation of primitively realisable bond graphs in terms of chordless odd loops and forbidden induced subgraphs is given. It is shown how to construct a primitive network equivalent to a given primitively realisable bond graph.

Odd rings and tunneling modes in glasses

Tunneling modes, elementary excitations of a large class of glasses, are local dynamical signatures of disorder. There is one tunneling mode per odd loop (a necklace through odd rings in the network), decoupled from other loops, and tunneling is forced by gauge invariance of the structure, the symmetry of disorder. Absence of tunneling modes in trivalent glasses (a-As or B 2O 3) is a notable consequence of this model. It is possible to decompose topologically a tetravalent network into a trivalent network, and to add a large proportion of boroxol rings with their characteristic but different dynamical signature.

Local subgroups of the Monster and odd code loops

The main result of this work is an explicit construction of p p -local subgroups of the Monster, the largest sporadic simple group. The groups constructed are the normalizers in the Monster of certain subgroups of order 3 2 3^{2} , 5 2 5^{2} , and 7 2 7^{2} and have shapes \[ 3 2 + 5 + 10 ⋅ ( M 11 × G L ( 2 , 3 ) ) , 5 2 + 2 + 4 ⋅ S 3 × G L ( 2 , 5 ) ) , and 7 2 + 1 + 2 ⋅ G L ( 2 , 7 ) {3^{2 + 5 + 10}}\cdot ({M_{11}} \times GL(2,3)),\quad {5^{2 + 2 + 4}}\cdot {S_3} \times GL(2,5)),\quad {\text {and}}{7^{2 + 1 + 2}}\cdot GL(2,7) \] . These groups result from a general construction which proceeds in three steps. We start with a self-orthogonal code C C of length n n over the field F p {\mathbb {F}_p} , where p p is an odd prime. The first step is to define a code loop L L whose structure is based on C C . The second step is to define a group N N of permutations of functions from F p 2 \mathbb {F}_p^2 to L L . The final step is to show that N N has a normal subgroup K K of order p 2 {p^2} . The result of this construction is the quotient group N / K N/K of shape p 2 + m + 2 m ( S × G L ( 2 , p ) ) {p^{2 + m + 2m}}(S \times GL(2,p)) , where m + 1 = dim ⁡ ( C ) m + 1 = \dim (C) and S S is the group of permutations of Aut ( C ) \text {Aut}(C) . To show that the groups we construct are contained in the Monster, we make use of certain lattices Λ ( C ) \Lambda (C) , defined in terms of the code C C . One step in demonstrating this is to show that the centralizer of an element of order p p in N / K N/K is contained in the centralizer of an element of order p p in the Monster. The lattices are useful in this regard since a quotient of the automorphism group of the lattice is a composition factor of the appropriate centralizer in the Monster. This work was inspired by a similar construction using code loops based on binary codes that John Conway used to construct a subgroup of the Monster of shape 2 2 + 11 + 22 ⋅ ( M 24 × G L ( 2 , 2 ) ) {2^{2 + 11 + 22}}\cdot ({M_{24}} \times GL(2,2)) .

The K-theory localization of loops on an odd sphere and applications

K-theory localization of an unstable odd sphere is constructed by Mahowald and Thompson in [8]. Earlier work on unstable K-theory localization includes Bousfield’s construction of the K-theory localization of infinite loop spaces in [4] and Mislin’s construction of the K-theory localization of Eilenberg-MacLane spaces in [13]. The con- struction of Mislin demonstrates that the unstable K-theory localization functor does not commute with taking loops on a space, nor does it preserve the connectivity of a space. This being the case, we note that the K-theory localization of loops on an odd sphere cannot be directly given by knowing the K-theory localization of an odd sphere. In recent work Bousfield avoids this difficulty by defining a new vi localization functor which behaves well with respect to fibrations and then shows that it is closely related to the unstable K-theory localization functor. In this paper a more direct approach will be taken to construct the K-theory localiza- tion of loops on an odd sphere and double loops on an odd sphere. The construction and proof is a generalization of the results of Mahowald and Thompson in [IS]. As an application, these results will be used to construct the K-theory localization of the fiber of the Hopf map. Construction and Results: We will begin by summarizing the construction of the K-theory localization of loops on an odd sphere done in [S]. By [14] the localization with respect to real and complex K-theory give the same result. Throughout this paper K-theory will refer to complex K-theory. For simplicity, we will take the localization with respect to KCpJ at each prime separately, where K,,, denotes p local complex K-theory. These localiza- tions may then be pieced together to give the K-theory localization. Let F, denote the homotopy fiber of the Snaith map where QX = C2= C”X, q = 2p - 2, and B, denotes a stunted BXP, localized at p with bottom cell in dimension m. The inclusion map ii :S2”+’ -+ QS2”+’ lifts to a map ji:S”‘+i -+ F,. Mahowald and Thompson show in [S] that the map jr induces an isomor- phism in p local K-theory. This is the first step in showing that their construction is the K-theory localization of S2”+ ‘. Now let G, denote the homotopy fiber of the localized Snaith map

Entanglements in glass

Ground state and elementary excitations (tunnelling modes) in glass are obtained from an analysis of its symmetry, a local gauge invariance. The configuration of glass is represented as a discrete fiber bundle. The base space is a continuous random network, standard model of the structure of covalent glasses. The connection is determined naturally by the elasticity of the network. The bundle is non-trivial, the elastic connection is entangled in one of two ways. Sources of non-triviality are closed loops, threading through odd rings in the network. To restore gauge invariance, tunnelling must occur between the two possible configurations about an odd loop. Entanglement and elementary excitations are labelled by permutations of the covalent bonds incident on an atom.

TOPOLOGICAL AND SCALING PROPERTIES OF LINE DEFECTS IN Ni-Mo AMORPHOUS FILMS

Odd loops of line defects were firstly found in the heavily irradiated amorphous films. A developed defect usually comprises two types of enclosed curves with different charges. Topologically, these defects are one-dimensional self-avoiding manifolds with variable connectivity. It is revealed that an attractive self-avoiding reaction and point-like defects dominate the evolution behavior of line defects. Scaling analyses show that both types of line defects are of statistical self-similarity with fractal dimensions between 1 and 2. Moreover, A self-consistent theory via self-avoiding tethered manifolds is proposed to account for the static and dynamic properties of the observed defects.

A general framework for reason maintenance

There are several different kinds of reason-maintenance system in existence, which provide rather different functionalities. I present a general structure that subsumes most such systems, and that allows some new behaviors to emerge. The general framework is based on logic-style clauses (disjunctions of literals) instead of justifications. Literals are tagged with labels that say what assumption sets make them true and false. Nonmonotonicity is implemented by allowing clauses to contain disjuncts of the form L p, which supports propagation through a clause whenever p is not known to be true. The resulting system supports two popular styles of dependency-directed backtracking, using nogoods and assumption retraction. Assumption retraction does not require a separate contradiction-elimination phase, but occurs automatically during label propagation. Label propagation can be achieved by the usual variants of Boolean constraint propagation, provided there are no “odd loops” through the clauses, and it can be shown that the system itself never creates odd loops.

The Steady and Oscillating States of a Proportioning Network

A steady state for a proportioning network is a dynamic state in which neither the node values nor the branch values vary with time. However, it is not required that the flows in opposite directions in a given branch be the same, as is the case for a balanced state. Every proportioning network has at least one steady state. Those branches that have nonzero flows under a given steady but not balanced state induce a bipartite subnetwork. A necessary condition for a proportioning network to have an infinity of steady states for every choice of its (positive) node values is that it contain a complete bipartite subnetwork M with at least two nodes on each side of M. A sufficient condition is that it contain such an M in such a fashion that every node not in M that is adjacent to a node of M is also adjacent to another node not in M. On the other hand, in order for a proportioning network to have no more than a finite number of steady states for each choice of its node values, it is necessary and sufficient that each of its components have no even loops and at most one odd loop. An oscillating state is a dynamic state in which every branch flow keeps reversing direction but remains fixed in magnitude as time progresses. A tree cannot have an oscillating state. Necessary and sufficient conditions on the initial branch values are established for the existence of an oscillating state. Also, to every unbalanced oscillating state there corresponds one or more balanced states, and those balanced states are asymptotically unstable.

Wavefunctions of identical particles

We present a description of the quantum mechanical states of a system of n indistinguishable particles moving on a manifold M by C/S2- valued functions ψ′ defined on the configuration space Mn/Sn. These functions satisfy one of two homotopy conditions, which characterize the particles as bosons or fermions. Any closed curve of Mn/Sn which does not intersect the diagonals can be classified as even or odd according to whether its lifts to Mn have end points in Mn which are even or odd permutations of each other. For bosons, ψ′ must map any such closed curve which also avoids kerψ′ onto an even number of basic loops of (C−{0})/S2. For fermions, ψ′ must map such even loops of Mn/Sn onto an even number, and odd loops onto an odd number, of basic loops of (C−{0})/S2.

A Topological Procedure for Converting a Bond Graph to a Linear Graph

A procedure for converting causally assigned bond graphs into corresponding linear graphs is presented. Topological relations between bond graphs and linear graphs are stipulated. Correspondences between bonds of a bond graph and edges of a system graph, power flows on bonds and orientation of edges, and a causal assignment and the selection of a tree are discussed. Special consideration is given to the uniqueness of the results, odd loops, and causal loops.