General Extension Research Articles

On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel

Consider a K-user flat fading MIMO interference channel where the kth transmitter (or receiver) is equipped with M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> (respectively N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) antennas. If an exponential (in K) number of generic channel extensions are used either across time or frequency, Cadambe and Jafar [1] showed that the total achievable degrees of freedom (DoF) can be maximized via interference alignment, resulting in a total DoF that grows linearly with A even if M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> are bounded. In this work we consider the case where no channel extension is allowed, and establish a general condition that must be satisfied by any degrees of freedom tuple (d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ....d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sub> ) achievable through linear interference alignment. For a symmetric system with M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = M, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = N, d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = d for all k, this condition implies that the total achievable DoF cannot grow linearly with K, and is in fact no more than K(M + N)/(K + 1). We also show that this bound is tight when the number of antennas at each transceiver is divisible by d, the number of data streams per user.

Ergodic infinite group extensions of geodesic flows on translation surfaces

We show that generic infinite group extensions of geodesic flows on square tiled translation surfaces are ergodic in almost every direction, subject to certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown that certain concrete staircases, covers of square-tiled surfaces, are not ergodic in almost every direction. In contrast we show the almost sure ergodicity of other concrete staircases. An appendix provides a combinatorial approach for the study of square-tiled surfaces.

Projective maximal families of orthogonal measures with large continuum

ORNQUIST Abstract: We study maximal orthogonal families of Borel probability measures on 2 ! (abbreviated m.o. families) and show that there are generic extensions of the constructible universe L in which each of the

Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials

We prove that the monoid of generic extensions of finite dimensional nilpotent $k[T]$-modules is isomorphic to the monoid of partitions (with addition of partitions). Moreover we give a combinatorial algorithm that calculates constant terms of classical Hall polynomials.

Presenting degenerate Ringel-Hall algebras of type B

We give a presentation for the degenerate Ringel-Hall algebras of type B by studying the corresponding generic extension monoid algebras. As an application, it is shown that the degenerate Ringel-Hall algebras of type B admit multiplicative bases.

Erratum to: Revisiting the global electroweak fit of the Standard Model and beyond with Gfitter

The global fit of the Standard Model to electroweak precision data, routinely performed by the LEP electroweak working group and others, demonstrated impressively the predictive power of electroweak unification and quantum loop corrections. We have revisited this fit in view of (i) the development of the new generic fitting package Gfitter, (ii) the insertion of constraints from direct Higgs searches at LEP and the Tevatron, and (iii) a more thorough statistical interpretation of the results. Gfitter is a modular fitting toolkit, which features predictive theoretical models as independent plugins, and a statistical analysis of the fit results using toy Monte Carlo techniques. The state-of-the-art electroweak Standard Model is fully implemented, as well as generic extensions to it. This paper introduces the Gfitter project, and presents state-of-the-art results for the global electroweak fit in the Standard Model, and for a model with an extended Higgs sector (2HDM). Numerical and graphical results for fits with and without including the constraints from the direct Higgs searches at LEP and Tevatron are given. Perspectives for future colliders are analysed and discussed. Including the direct Higgs searches, we find M_H=(116.4 +18.3 -1.3) GeV, and the 2sigma and 3sigma allowed regions [114,145] GeV and [[113,168] and [180,225]] GeV, respectively. For the strong coupling strength at fourth perturbative order we obtain alpha_S(M_Z)=0.1193 +0.0028 -0.0027(exp) +- 0.0001(theo). Finally, for the mass of the top quark, excluding the direct measurements, we find m_t=(178.2 +9.8 -4.2) GeV. In the 2HDM we exclude a charged-Higgs mass below 240 GeV at 95% confidence level. This limit increases towards larger tan(beta), where e.g., M_H+-<780 GeV is excluded for tan(beta)=70.

Superatomic Boolean algebras constructed from strongly unbounded functions

Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf(η) = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal B$\end{document} such that \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{ht}(\mathcal B) = \eta + 1$\end{document}, \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{wd}_{\alpha }(\mathcal B) = \kappa$\end{document} for every α < η and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{wd}_{\eta }(\mathcal B) = \lambda$\end{document}(i.e., there is a locally compact scattered space with cardinal sequence 〈κ〉η⌢︁〈λ〉). Especially, \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\langle {\omega }\rangle _{{\omega }_1}{}^{\smallfrown } \langle {\omega }_3\rangle$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\langle {\omega }_1\rangle _{{\omega }_2}{}^{\smallfrown } \langle {\omega }_4\rangle$\end{document} can be cardinal sequences of superatomic Boolean algebras.

Hechler's Theorem for tall analytic P-ideals

AbstractWe prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal (coded in the ground model) a cofinal subset of is order isomorphic to (Q, ≤).

On the Weak Reflection Principle

The Weak Reflection Principle for ω 2 \omega _2 , or WRP ( ω 2 ) \textrm {WRP}(\omega _2) , is the statement that every stationary subset of P ω 1 ( ω 2 ) P_{ \omega _1}(\omega _2) reflects to an uncountable ordinal in ω 2 \omega _2 . The Reflection Principle for ω 2 \omega _2 , or RP ( ω 2 ) \textrm {RP}(\omega _2) , is the statement that every stationary subset of P ω 1 ( ω 2 ) P_{ \omega _1 } ( \omega _2 ) reflects to an ordinal in ω 2 \omega _2 with cofinality ω 1 \omega _1 . Let κ \kappa be a κ + \kappa ^+ -supercompact cardinal and assume 2 κ = κ + 2^{\kappa } = \kappa ^+ . Then there exists a forcing poset P \mathbb {P} which collapses κ \kappa to become ω 2 \omega _2 , and ⊩ P WRP ( ω 2 ) ∧ ¬ RP ( ω 2 ) \Vdash _{\mathbb {P}} \textrm {WRP}(\omega _2) \land \neg \textrm {RP}(\omega _2) .

Access control via belnap logic

Access control to IT systems increasingly relies on the ability to compose policies. Hence there is benefit in any framework for policy composition that is intuitive, formal (and so “analyzable” and “implementable”), expressive, independent of specific application domains, and yet able to be extended to create domain-specific instances. Here we develop such a framework based on Belnap logic. An access-control policy is interpreted as a four-valued predicate that maps access requests to either grant , deny , conflict , or unspecified -- the four values of the Belnap bilattice. We define an expressive access-control policy language PBel, having composition operators based on the operators of Belnap logic. Natural orderings on policies are obtained by lifting the truth and information orderings of the Belnap bilattice. These orderings lead to a query language in which policy analyses, for example, conflict freedom, can be specified. Policy analysis is supported through a reduction of the validity of policy queries to the validity of propositional formulas on predicates over access requests. We evaluate our approach through firewall policy and RBAC policy examples, and discuss domain-specific and generic extensions of our policy language.

Privacy preservation with X.509 standard certificates

Privacy preservation has become an essential requirement in today’s computing environment; abuse based on anonymity and user-controlled pseudonyms is a serious problem. For prompt deployment in legacy information systems, it would be desirable to develop a new method in the standard paradigm. This paper investigates practical methods for privacy preservation with X.509 standard certificates by providing conditional traceability for both identity and attribute certificates in the legacy systems. We separate certificate authorities, one for verifying identities and the other for validating contents, in a blinded manner without requiring a trusted third party. We design a concrete method with its more generic and applicative extensions, and prove security formally. We also evaluate performance through rigorous experiments and discuss possible applications.

Openly generated Boolean algebras and the Fodor-type reflection principle

We prove that the Fodor-type Reection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is ℵ2-projective. Previously it was known that this characterization of openly generated Boolean algebras follows from Axiom R. Since FRP is preserved by c.c.c. generic extension, we conclude in particular that this characterization is consistent with any set-theoretic assertion forcable by a c.c.c. poset starting from a model of FRP. A crucial step of the proof of the main result is to show that FRP implies Shelah’s Strong Hypothesis (SSH). In particular, we obtain that FRP implies the Singular Cardinals Hypothesis (SCH). Continuing Rinot [17], we also establish some new characterizations of SSH in terms of topological reection theorems.

The complex local mean decomposition

The local mean decomposition (LMD) has been recently developed for the analysis of time series which have nonlinearity and nonstationarity. The smoothed local mean of the LMD surpasses the cubic spline method used by the empirical mode decomposition (EMD) to extract amplitude and frequency modulated components. To process complex-valued data, we propose complex LMD, a natural and generic extension to the complex domain of the original LMD algorithm. It is shown that complex LMD extracts the frequency modulated rotation and envelope components. Simulations on both artificial and real-world complex-valued signals support the analysis.

SLHAplus: A library for implementing extensions of the standard model

We provide a library to facilitate the implementation of new models in codes such as matrix element and event generators or codes for computing dark matter observables. The library contains an SLHA reader routine as well as diagonalisation routines. This library is available in CalcHEP and micrOMEGAs. The implementation of models based on this library is supported by LanHEP and FeynRules. Program summary Program title: SLHAplus_1.3 Catalogue identifier: AEHX_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6283 No. of bytes in distributed program, including test data, etc.: 52 119 Distribution format: tar.gz Programming language: C Computer: IBM PC, MAC Operating system: UNIX (Linux, Darwin, Cygwin) RAM: 2000 MB Classification: 11.1 Nature of problem: Implementation of extensions of the standard model in matrix element and event generators and codes for dark matter observables. Solution method: For generic extensions of the standard model we provide routines for reading files that adopt the standard format of the SUSY Les Houches Accord (SLHA) file. The procedure has been generalized to take into account an arbitrary number of blocks so that the reader can be used in generic models including non-supersymmetric ones. The library also contains routines to diagonalize real and complex mass matrices with either unitary or bi-unitary transformations as well as routines for evaluating the running strong coupling constant, running quark masses and effective quark masses. Running time: 0.001 sec

Large loop effects of extra supersymmetric Higgs doublets toCPviolation inB0mixing

We consider more than one pair of SU(2)_L doublet Higgs supermultiplets in a generic supersymmetric extension of the standard model, and calculate their one-loop contributions to the soft mass insertions delta_{LL} etc. We find that if large supersymmetry breaking in this sector is realized, the loop effects can give rise to large contributions to the soft mass insertions, meaning that they We apply our result to a recently proposed model based on the discrete Q_6 family group, and calculate the non-diagonal matrix element M_{12} of the neutral meson systems. We focus our attention on the extra phases phi_{d,s}^Delta in B_{d,s}-mixing and flavor-specific CP-asymmetries a_{sl}^{d,s} in neutral B decays and obtain values that can be about one order of magnitude larger than the standard model predictions. Our final results are comparable with the recent experimental observations at D0 and CDF, but they are still about a factor of 5 smaller than the recently measured dimuon asymmetry from D0.

On coding uncountable sets by reals

AbstractIf A ⊆ ω1, then there exists a cardinal preserving generic extension 𝕃[A ][x ] of 𝕃[A ] by a real x such that1) A ∈ 𝕃[x ] and A is Δ1HC (x) in 𝕃[x ];2) x is minimal over 𝕃[A ], that is, if a set Y belongs to 𝕃[x ], then either x ∈ 𝕃[A, Y ] or Y ∈ 𝕃[A ].The forcing we use implicitly provides reshaping of the given set A (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Absolute E-rings

A ring R with 1 is called an E-ring if EndZR is ring-isomorphic to R under the canonical homomorphism taking the value 1σ for any σ∈EndZR. Moreover R is an absolute E-ring if it remains an E-ring in every generic extension of the universe. E-rings are an important tool for algebraic topology as explained in the introduction. The existence of an E-ring R of each cardinality of the form λℵ0 was shown by Dugas, Mader and Vinsonhaler (1987) [9]. We want to show the existence of absolute E-rings. It turns out that there is a precise cardinal-barrier κ(ω) for this problem: (The cardinal κ(ω) is the first ω-Erdős cardinal defined in the introduction. It is a relative of measurable cardinals.) We will construct absolute E-rings of any size λ<κ(ω). But there are no absolute E-rings of cardinality ⩾κ(ω). The non-existence of huge, absolute E-rings ⩾κ(ω) follows from a recent paper by Herden and Shelah (2009) [24] and the construction of absolute E-rings R is based on an old result by Shelah (1982) [31] where families of absolute, rigid colored trees (with no automorphism between any distinct members) are constructed. We plant these trees into our potential E-rings with the aim to prevent unwanted endomorphisms of their additive group to survive. Endomorphisms will recognize the trees which will have branches infinitely often divisible by primes. Our main result provides the existence of absolute E-rings for all infinite cardinals λ<κ(ω), i.e. these E-rings remain E-rings in all generic extensions of the universe (e.g. using forcing arguments). Indeed all previously known E-rings (Dugas, Mader and Vinsonhaler, 1987 [9]; Göbel and Trlifaj, 2006 [23]) of cardinality ⩾2ℵ0 have a free additive group R+ in some extended universe, thus are no longer E-rings, as explained in the introduction. Our construction also fills all cardinal-gaps of the earlier constructions (which have only sizes λℵ0). These E-rings are domains and as a by-product we obtain the existence of absolutely indecomposable abelian groups, compare Göbel and Shelah (2007) [22].

Systematic and taxomonic revaluation of four little known Asian agamid species, Calotes kingdonwardi Smith, 1935, Japalura kaulbacki Smith, 1937, Salea kakhienensis Anderson, 1879 and the monotypic genus Mictopholis Smith, 1935 (Reptilia: Agamidae)

The systematic status of many Asian Draconine agamids has long been in dispute. Herein, four such species, Mictopholis austeniana, Japalura kaulbacki, Calotes kingdonwardi and Salea kakhienensis are examined on the basis of external morphological characters. The monotypic genus Mictopholis was compared to other Asian Draconine genera and found to be indistinguishable from Pseudocalotes, with which it is here considered a synonym. Japalura kaulbacki is compared to other members of the genus Japalura as well as other similar species. Based on external morphology it is found to be separable from Japalura and conspecific with Calotes kingdonwardi, under which it is considered a junior subjective synonym. Salea kakhienensis is redefined morphologically based on nontype material and shown to represent a close member of this group. C. kingdonwardi is most similar to Salea kakhienensis both of which share a complement of characters with M. austeniana. The generic placement of S. kakhienensis relative to Salea, both with strongly overlapping synapomorphic characters is briefly discussed with respect to biogeographical implications that strongly support the exclusion of this species from the genus. Mictopholis austeniana, Calotes kingdonwardi and Salea kakhienensis are redescribed in detail and transferred to Pseudocalotes. The inclusion of these three species provides a generic range extension of approximately 800 km north-west of the previously considered range. The nomen Oriocalotes discolor is considered a primary objective synonym of Pseudocalotes kakhienensis new comb. and the systematic status of Calotes kingdonwardi bapoensis is briefly discussed.

A generic attribute extension to OTF and its use for MPI replay

Data formats are important components for parallel event tracing tools used for debugging and performance analysis. This paper presents a generic extension mechanism for the Open Trace Format (OTF) that allows to add arbitrary data to the existing event data types. This avoids the need to frequently adapt the data format and the library API to accommodate new usage scenarios. The replay of MPI communication is demonstrated as a real-world example that requires an extension. Several other application scenarios that would benefit from additional data about certain event types are mentioned.

On almost precipitous ideals

With less than 0# two generic extensions ofL are identified: one in which \({\aleph_1}\), and the other \({\aleph_2}\), is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it is shown that if δ is a Woodin cardinal and there is an \({f:\omega_1 \to \omega_1}\) with \({\|f\|=\omega_2}\), then after \({Col(\aleph_2,\delta)}\) there is a normal precipitous ideal over \({\aleph_1}\). The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal.