scholarly journals Equivalence Relations of Permutations Generated by Constrained Transpositions

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Stephen Linton ◽  
James Propp ◽  
Tom Roby ◽  
Julian West
Keyword(s):  
General Setting ◽  
Large Family ◽  
Equivalence Classes ◽  
The Other ◽  
Equivalence Relations ◽  
Integer Sequences ◽  
Identity Permutation ◽  
Nous Trouvons ◽  
International Audience ◽  
Tribonacci Numbers

International audience We consider a large family of equivalence relations on permutations in $S_n$ that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one can be obtained from the other by a sequence of pattern-replacing moves of prescribed form; however, we limit our focus to patterns where two elements are transposed, conditional upon the presence of a third element of suitable value and location. For some relations of this type, we compute the number of equivalence classes, determine how many $n$-permutations are equivalent to the identity permutation, or characterise this equivalence class. Although our results include familiar integer sequences (e.g., Catalan, Fibonacci, and Tribonacci numbers) and special classes of permutations (layered, connected, and $123$-avoiding), some of the sequences that arise appear to be new. Nous considérons une famille de relations d’équivalence sur l'ensemble $S_n$ des permutations, qui généralisent les relations de Knuth liées à la correspondance Robinson-Schensted. Dans notre contexte général, deux permutations sont considérées comme équivalentes si l'une peut être obtenue de l'autre auprès d'une séquence de remplacements d'un motif par un autre selon des règles précisées. Désormais, nous ne considérons dans l’œuvre actuelle que les motifs qui correspondent à la transposition de deux éléments, conditionné sur la présence d'un élément de valeur et de position approprié. Pour plusieurs exemples de ce problème, nous énumérons les classes d'équivalence, nous déterminons combien de permutations sur $n$ éléments sont équivalentes à l'identité, ou nous précisons la forme des éléments dans cette dernière classe. Bien que nos résultats retrouvent des séquences des entiers très bien connues (nombres de Catalan, de Fibonacci, de Tribonacci...) ainsi que des classes de permutations déjà étudiées (en couches, connexes, sans motif $123$), nous trouvons également des séquences qui paraissent être nouvelles.

Incest Offences and Alcoholism

1974 ◽  
Vol 14 (2) ◽  
pp. 124-128 ◽  
Author(s):  
M. Virkkunen
Keyword(s):  
Sexual Behaviour ◽  
Psychiatric Hospitalization ◽  
Large Family ◽  
Sexual Attitude ◽  
Living Conditions ◽  
The Other ◽  
Alcoholic Drinks ◽  
The Relationship ◽  
At Home

The purpose of this study was to clarify whether alcoholic incest offenders differ from other criminals who commit these offences. The series consisted of 45 cases of incest, of which 22 cases (48.9 per cent) gave an indication of alcoholism in the offender. The alcoholics showed more evidence of previous criminal offences, and this was especially true when considering acts of violence only. The alcoholics had also exhibited more often than the others aggressive features at home before the detection of incest. Statistically, significant differences were not arrived at as to depression, psychotic disturbances, intellectual defects, problems of jealousy, psychiatric hospitalization, and earlier sexual behaviour. The spouse had a rejective sexual attitude towards the offender in alcoholic cases more frequently than in other cases. The cause of this appeared to be mainly disgust at the abuse of alcoholic drinks and its consequences, as well as the result of a large family and/or poor living conditions. In more than half of the cases of incest in both groups actual intercourse had taken place. Generally, the relationship had, however, started by only touching sexual organs and so forth. According to the offender the victim had shown activity in one-third of the cases of alcoholics. The alcoholic offender tended to be under the influence of alcohol at least at the beginning of the relationship more often than the non-alcoholic person. Offences or an offence were reported by the victim or the offender's spouse in the cases of alcoholics more often than in the other cases; then the informer was usually an outsider. However, the victim's and the spouse's fear of the offender was one reason for concealment when the alcoholics were involved.

scholarly journals Quantum Physical Unclonable Functions: Possibilities and Impossibilities

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 475
Author(s):  
Myrto Arapinis ◽  
Mahshid Delavar ◽  
Mina Doosti ◽  
Elham Kashefi
Keyword(s):  
Large Family ◽  
Quantum States ◽  
The Other ◽  
Quantum Game ◽  
Physical Unclonable Function ◽  
Physical Unclonable Functions ◽  
Quantum Analogue ◽  
Universal Quantum ◽  
Different Levels ◽  
Comprehensive Study

A Physical Unclonable Function (PUF) is a device with unique behaviour that is hard to clone hence providing a secure fingerprint. A variety of PUF structures and PUF-based applications have been explored theoretically as well as being implemented in practical settings. Recently, the inherent unclonability of quantum states has been exploited to derive the quantum analogue of PUF as well as new proposals for the implementation of PUF. We present the first comprehensive study of quantum Physical Unclonable Functions (qPUFs) with quantum cryptographic tools. We formally define qPUFs, encapsulating all requirements of classical PUFs as well as introducing a new testability feature inherent to the quantum setting only. We use a quantum game-based framework to define different levels of security for qPUFs: quantum exponential unforgeability, quantum existential unforgeability and quantum selective unforgeability. We introduce a new quantum attack technique based on the universal quantum emulator algorithm of Marvin and Lloyd to prove no qPUF can provide quantum existential unforgeability. On the other hand, we prove that a large family of qPUFs (called unitary PUFs) can provide quantum selective unforgeability which is the desired level of security for most PUF-based applications.

Patrick Maynard Stuart Blackett, Baron Blackett, of Chelsea, 18 November 1897 - 13 July 1974

1975 ◽  
Vol 21 ◽  
pp. 1-115 ◽  
Keyword(s):  
Church Of England ◽  
Large Family ◽  
The Other ◽  
Future Career ◽  
The Family ◽  
The Future ◽  
Two Generations ◽  
Indian Mutiny ◽  
The Church ◽  
Deep Interest

Patrick Maynard Stuart Blackett was born in Kensington, London, on 18 November 1897. His father, Arthur Stuart Blackett, was a stockbroker, although apparently not by inclination since his great interests were in literature and nature. Patrick was the only boy but had an elder and younger sister; one trained and practised as an architect in the 1920s, until she married, and the other became an industrial psychologist and then a psychoanalyst. For the previous two generations the family had been associated with the Church of England. Patrick’s grandfather had been Vicar of the church in Woburn Square (now demolished), and was the Vicar of St Andrew’s, Croydon, at the time of his death. He had twice married and Arthur Stuart was one of a large family, two of whom went into the Church, whilst another became a missionary in India. Patrick’s great-grandfather came from Hamsterley in Co. Durham of a farming family. He moved to London and his children were baptised in St Saviour’s Church, Southwark (now Southwark Cathedral). The future career and interests of Patrick seem to have more association with his maternal descent. His mother, Caroline Frances Maynard, was the daughter of Major Charles Maynard, R.A., who served in India at the time of the Indian Mutiny. William Maynard, a brother of Charles, was also associated with India as a tea planter. The source of Patrick’s deep interest in Indian affairs has this association; so does his early naval career and his continued absorption in military affairs—in addition to the army career of his grandfather there was an earlier tradition of naval service in the Maynard family.

scholarly journals Equivalence Projective Simulation as a Framework for Modeling Formation of Stimulus Equivalence Classes

2020 ◽  
Vol 32 (5) ◽  
pp. 912-968 ◽  
Author(s):  
Asieh Abolpour Mofrad ◽  
Anis Yazidi ◽  
Hugo L. Hammer ◽  
Erik Arntzen
Keyword(s):  
Stimulus Equivalence ◽  
Human Subjects ◽  
Network Models ◽  
Equivalence Classes ◽  
Equivalence Relations ◽  
Learning Context ◽  
Neural Network Models ◽  
Equivalence Theory ◽  
Hypothetical Experiment ◽  
Theory Research

Stimulus equivalence (SE) and projective simulation (PS) study complex behavior, the former in human subjects and the latter in artificial agents. We apply the PS learning framework for modeling the formation of equivalence classes. For this purpose, we first modify the PS model to accommodate imitating the emergence of equivalence relations. Later, we formulate the SE formation through the matching-to-sample (MTS) procedure. The proposed version of PS model, called the equivalence projective simulation (EPS) model, is able to act within a varying action set and derive new relations without receiving feedback from the environment. To the best of our knowledge, it is the first time that the field of equivalence theory in behavior analysis has been linked to an artificial agent in a machine learning context. This model has many advantages over existing neural network models. Briefly, our EPS model is not a black box model, but rather a model with the capability of easy interpretation and flexibility for further modifications. To validate the model, some experimental results performed by prominent behavior analysts are simulated. The results confirm that the EPS model is able to reliably simulate and replicate the same behavior as real experiments in various settings, including formation of equivalence relations in typical participants, nonformation of equivalence relations in language-disabled children, and nodal effect in a linear series with nodal distance five. Moreover, through a hypothetical experiment, we discuss the possibility of applying EPS in further equivalence theory research.

Spanning Properties of Yao and 𝜃-Graphs in the Presence of Constraints

2019 ◽  
Vol 29 (02) ◽  
pp. 95-120 ◽  
Author(s):  
Prosenjit Bose ◽  
André van Renssen
Keyword(s):  
Line Segment ◽  
Large Family ◽  
Upper Bounds ◽  
The Other ◽  
Additional Property ◽  
Graph Partitions ◽  
Set Of Points ◽  
The Given

We present improved upper bounds on the spanning ratio of constrained [Formula: see text]-graphs with at least 6 cones and constrained Yao-graphs with 5 or at least 7 cones. Given a set of points in the plane, a Yao-graph partitions the plane around each vertex into [Formula: see text] disjoint cones, each having aperture [Formula: see text], and adds an edge to the closest vertex in each cone. Constrained Yao-graphs have the additional property that no edge properly intersects any of the given line segment constraints. Constrained [Formula: see text]-graphs are similar to constrained Yao-graphs, but use a different method to determine the closest vertex. We present tight bounds on the spanning ratio of a large family of constrained [Formula: see text]-graphs. We show that constrained [Formula: see text]-graphs with [Formula: see text] ([Formula: see text] and integer) cones have a tight spanning ratio of [Formula: see text], where [Formula: see text] is [Formula: see text]. We also present improved upper bounds on the spanning ratio of the other families of constrained [Formula: see text]-graphs. These bounds match the current upper bounds in the unconstrained setting. We also show that constrained Yao-graphs with an even number of cones ([Formula: see text]) have spanning ratio at most [Formula: see text] and constrained Yao-graphs with an odd number of cones ([Formula: see text]) have spanning ratio at most [Formula: see text]. As is the case with constrained [Formula: see text]-graphs, these bounds match the current upper bounds in the unconstrained setting, which implies that like in the unconstrained setting using more cones can make the spanning ratio worse.

Regent Results in Comma-Free Codes

1963 ◽  
Vol 15 ◽  
pp. 178-187 ◽  
Author(s):  
B. H. Jiggs
Keyword(s):  
Equivalence Class ◽  
Cyclic Permutation ◽  
Equivalence Classes ◽  
The Other ◽  
Complete Class

A set D of k-letter words is called a comma-free dictionary (2), if whenever (a1a2 . . . ak) and (b1b2 . . . bk) are in D, the "overlaps" (a2a3 . . . akb1), (a3a4 . . . akb1b2), . . . , (akb1 . . . bk-1) are not in D. We say that two k-letter words are in the same equivalence class if one is a cyclic permutation of the other. An equivalence class is called complete if it contains k distinct members. Comma-freedom is violated if we choose words from incomplete equivalence classes, or if more than one word is chosen from the same complete class.

Approximate equivalence of group actions

2017 ◽  
Vol 38 (4) ◽  
pp. 1201-1237 ◽  
Author(s):  
ANDREAS NÆS AASERUD ◽  
SORIN POPA
Keyword(s):  
Group Actions ◽  
The Other ◽  
Equivalence Relations ◽  
Orbit Equivalence ◽  
Usual Type ◽  
New Concepts ◽  
Probability Spaces ◽  
Measure Preserving Actions

We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining conditions. We compare them with the other existing equivalence relations between group actions, and study the usual type of rigidity questions around these new concepts (superrigidity, calculation of invariants, etc).

scholarly journals Polynomial Solution to the Position Analysis of Two Assur Kinematic Chains With Four Loops and the Same Topology

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Júlia Borràs ◽  
Raffaele Di Gregorio
Keyword(s):  
Polynomial Solution ◽  
Large Family ◽  
The Other ◽  
End Effector ◽  
Closed Loops ◽  
Kinematic Chains ◽  
Position Analysis ◽  
One To One ◽  
Actuated Joints

The direct position analysis (DPA) of a manipulator is the computation of the end-effector poses (positions and orientations) compatible with assigned values of the actuated-joint variables. Assigning the actuated-joint variables corresponds to considering the actuated joints locked, which makes the manipulator a structure. The solutions of the DPA of a manipulator one to one correspond to the assembly modes of the structure that is generated by locking the actuated-joint variables of that manipulator. Determining the assembly modes of a structure means solving the DPA of a large family of manipulators since the same structure can be generated from different manipulators. This paper provides an algorithm that determines all the assembly modes of two structures with the same topology that are generated from two families of mechanisms: one planar and the other spherical. The topology of these structures is constituted of nine links (one quaternary link, four ternary links, and four binary links) connected through 12 revolute pairs to form four closed loops.

scholarly journals BINARY PRIMITIVE HOMOGENEOUS SIMPLE STRUCTURES

2017 ◽  
Vol 82 (1) ◽  
pp. 183-207 ◽  
Author(s):  
VERA KOPONEN
Keyword(s):  
Algebraic Closure ◽  
The Other ◽  
Equivalence Relations ◽  
Complete Theory ◽  
Future Research ◽  
Random Structure ◽  
Homogeneous Structures ◽  
Image Position

AbstractSuppose that ${\cal M}$ is countable, binary, primitive, homogeneous, and simple. We prove that the SU-rank of the complete theory of ${\cal M}$ is 1 and hence 1-based. It follows that ${\cal M}$ is a random structure. The conclusion that ${\cal M}$ is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of ω-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures.

scholarly journals Lagrange's Theorem for Hopf Monoids in Species

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Marcelo Aguiar ◽  
Aaron Lauve
Keyword(s):  
Necessary Conditions ◽  
Generating Series ◽  
Nous Trouvons ◽  
International Audience ◽  
Binomial Transform ◽  
Hopf Monoid ◽  
Lagrange's Theorem

International audience We prove Lagrange's theorem for Hopf monoids in the category of connected species. We deduce necessary conditions for a given subspecies $\textrm{k}$ of a Hopf monoid $\textrm{h}$ to be a Hopf submonoid: each of the generating series of $\textrm{k}$ must divide the corresponding generating series of $\textrm{k}$ in ℕ〚x〛. Among other corollaries we obtain necessary inequalities for a sequence of nonnegative integers to be the sequence of dimensions of a Hopf monoid. In the set-theoretic case the inequalities are linear and demand the non negativity of the binomial transform of the sequence. Nous prouvons le théorème de Lagrange pour les monoïdes de Hopf dans la catégorie des espèces connexes. Nous déduisons des conditions nécessaires pour qu'une sous-espèce $\textrm{k}$ d'un monoïde de Hopf $\textrm{h}$ soit un sous-monoïde de Hopf: chacune des séries génératrices de $\textrm{k}$ doit diviser la série génératrice correspondante de $\textrm{h}$ dans ℕ〚x〛. Parmi d'autres corollaires nous trouvons des inégalités nécessaires pour qu'une suite d'entiers soit la suite des dimensions d'un monoïde de Hopf. Dans le cas ensembliste les inégalités sont linéaires et exigent que la transformée binomiale de la suite soit non négative.

Sign in / Sign up

Export Citation Format

Share Document