Double-partition Quantum Cluster Algebras

A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but subclasses have been studied previously by other authors. The algebras are indexed by double partitions or double flag varieties. Equivalently, they are indexed by broken lines $L$. By grouping together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis. This is the final version, where some arguments have been expanded and/or improved and several typos corrected. Full bibliographic details: Journal of Algebra (2012), pp. 172-203 DOI information: 10.1016/j.jalgebra.2012.09.015Comment: LaTeX 39 page

Linear versus spin: representation theory of the symmetric groups

We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$ with analogous normalized linear characters evaluated on the double partition $D(\xi)$. We also relate some natural filtration on the usual (linear) Kerov-Olshanski algebra of polynomial functions on the set of Young diagrams with its spin counterpart. Finally, we give a spin counterpart to Stanley formula for the characters of the symmetric groups.Comment: 41 pages. Version 2: new text about non-oriented (but orientable) map

Allowing content-based functionalities in segmentation-based coding schemes

This paper deals with the use of the segmentation tools and principles presented in [10] and [13] for allowing content-based functionalities. In this framework, means for supervised selection of objects in the scene are proposed. In addition, a technique for object tracking in the context of segmentation-based video coding is presented. The technique is independent of the type of segmentation approach used in the coding scheme. The algorithm relies on a double partition of the image that yields spatially homogeneous regions. This double partition permits to obtain the position and shape of the previous object in the current image while computing the projected partition. In order to demonstrate the potentialities of this algorithm, it is applied in a specific coding scheme so that content-based functionalities, such as selective coding, are allowed.Peer ReviewedPostprint (published version

Measuring dynamic stiffness of steel stud for lightweight double partition wall and sound insulation

Kevyillä kaksinkertaisilla väliseinärakenteilla voidaan saavuttaa kilpailukykyinen ääneneristävyys asuin- ja toimistorakennuksissa. Paras ääneneristävyys saavutetaan käyttämällä seinäpaneelien tuentana joustavaa teräsrankaa. Teorian mukaan tekemällä pystyrangasta joustava puristussuunnassa saavutetaan parempi ääneneristävyys. Testitulokset prototyyppirangoilla ovat olleet ristiriidassa tämän teorian kanssa. Rangan dynaamista jäykkyyttä käytetään yhtenä parametrina kaksoisrakenneseinän ääneneristävyyden ennustemallissa. Rangan dynaaminen jäykkyys voidaan selvittää kokeellisesti. Tässä työssä esitetään mittausmenetelmä, jolla dynaaminen jäykkyys selvitetään teräsrangan ja kuormamassan muodostaman massa-jousisysteemin ominaistaajuudesta. Systeemin herätteenä voidaan käyttää joko iskuvasaran impulssia tai täristimen jatkuvaa kohinaa. Mittausjärjestelmällä mitattiin kymmenen rankanäytettä yksinkertaisella ja kaksinkertaisella kiinnitystavalla. Tuloksista havaittiin, että kaksinkertaistamalla kiinnitysruuvien määrä, massa-jousisysteemin dynaaminen jäykkyys kasvoi keskimäärin 160 %. Mittaustulosten ja pohdintojen perusteella esitetään akustisesti paremman teräsrangan kehitysehdotus ja pohditaan kevytrakenneseinän muita kehityspolkuja ääneneristävyyden kannalta.A competitive sound insulation can achieved with light weight double partition walls compared to heavy alternatives. Best insulation can be attained using flexible steel studs as wall panel support. According to conventional theory the most compress flexible stud gives best results in sound insulation. Recent test results are in conflict with the theory. Dynamic stiffness of the steel stud is used as a parameter in double partition wall sound insulation prediction method. The dynamic stiffness can be experimentally measured. This thesis presents a measurement method which derives dynamic stiffness from the natural frequency of mass-spring system of steel stud and preload mass. Impulse hammer or shaker can be used as stimulus. Ten steel studs were measured using single and double screw fastenings. Doubling the number of fastenings increased the dynamic stiffness of the system by 160 % by average. A development proposal for steel studs is presented on the grounds of measurement results and speculations. Other development paths in the acoustics of light weight double partition walls are discussed

Classification of SUSY and non-SUSY Chiral Models from Abelian Orbifolds AdS/CFT

We classify compactifications of the type IIB superstring on AdS_{5} x S^{5}/\Gamma, where \Gamma is an abelian group of order n<= 12. Appropriate embedding of \Gamma in the isometry of S^5 yields both SUSY and non-SUSY chiral models that can contain the minimal SUSY standard model or the standard model. New non-SUSY three family models with \Gamma=Z_8 are introduced, which lead to the right Weinberg angle for TeV trinification.Comment: 12 pages, no figur

Adapted pairs in type AA and regular nilpotent elements

Let $\mathfrak g$ be a simple Lie algebra over an algebraically closed field $\bf k$ of characteristic zero and $\bf G$ its adjoint group. Let $\mathfrak q$ be a biparabolic subalgebra of $\mathfrak g$. The algebra $Sy(\mathfrak q)$ of semi-invariants on $\mathfrak q^*$ is polynomial in most cases, in particular when $\mathfrak g$ is simple of type $A$ or $C$. On the other hand $\mathfrak q$ admits a canonical truncation $\mathfrak q_{\Lambda}$ such that $Sy(\mathfrak q)=Sy(\mathfrak q_{\Lambda})=Y(\mathfrak q_{\Lambda})$ where $Y(\mathfrak q_{\Lambda})$ denotes the algebra of invariant functions on $\mathfrak q_{\Lambda}^*$. An adapted pair for $\mathfrak q_{\Lambda}$ is a pair $(h,\,\eta)\in \mathfrak q_{\Lambda}\times\mathfrak q_{\Lambda}^*$ such that $\eta$ is regular and $(ad\,h)\eta=-\eta$. In a previous paper of A. Joseph (2008) adapted pairs for every truncated biparabolic subalgebra $\mathfrak q_{\Lambda}$ of a simple Lie algebra $\mathfrak g$ of type $A$ were constructed and then provide Weierstrass sections for $Y(\mathfrak q_{\Lambda})$ in $\mathfrak q_{\Lambda}^*$. These latter are linear subvarieties $\eta+V$ of $\mathfrak q_{\Lambda}^*$ such that the restriction map induces an algebra isomorphism of $Y(\mathfrak q_{\Lambda})$ onto the algebra of regular functions on $\eta+V$. Here we show that for each of the adapted pairs $(h,\,\eta)$ constructed in the paper mentioned above one can express $\eta$ as the image of a regular nilpotent element $y$ of $\mathfrak g^*$ under the restriction to $\mathfrak q$. Since $y$ must be a $\bf G$ translate of the standard regular nilpotent element defined in terms of the already chosen set $\pi$ of simple roots, one may attach to $y$ a unique element of the Weyl group. Ultimately one can then hope to be able to describe adapted pairs (in general) through the Weyl group.Comment: This is a rewriting of the version submitted on the arXiv in June 201

A segmentation-based coding system allowing manipulation of objects (sesame)

We present a coding scheme that achieves, for each image in the sequence, the best segmentation in terms of rate-distortion theory. It is obtained from a set of initial regions and a set of available coding techniques. The segmentation combines spatial and motion criteria. It selects at each area of the image the most adequate criterion for defining a partition in order to obtain the best compromise between cost and quality. In addition, the proposed scheme is very suitable for addressing content-based functionalities.Peer ReviewedPostprint (published version