Faltings' local-global principle for the minimaxness of local cohomology modules

The concept of Faltings' local-global principle for the minimaxness of local cohomology modules over a commutative Noetherian ring $R$ is introduced, and it is shown that this principle holds at level 2. We also establish the same principle at all levels over an arbitrary commutative Noetherian ring of dimension not exceeding 3. These generalize the main results of Brodmann et al. in \cite{BRS}. Moreover, it is shown that if $M$ is a finitely generated $R$-module, $\frak a$ an ideal of $R$ and $r$ a non-negative integer such that $\frak a^tH^i_{\frak a}(M)$ is skinny for all $i<r$ and for some positive integer $t$, then for any minimax submodule $N$ of $H^r_{\frak a}(M)$, the $R$-module \Hom_R(R/\frak a, H^r_{\frak a}(M)/N) is finitely generated. As a consequence, it follows that the associated primes of $H^r_{\frak a}(M)/N$ are finite. This generalizes the main results of Brodmann-Lashgari \cite{BL} and Quy \cite{Qu}.Comment: 11 page

On the generalization of Faltings' Annihilator Theorem

Let $R$ be a commutative Noetherian ring and let $n$ be a non-negative integer. In this article, by using the theory of Gorenstein dimensions, it is shown that whenever $R$ is a homomorphic image of a Noetherian Gorenstein ring, then the invariants \inf\{i\in\nat_0|\, {\dim\Supp}(\fb^tH_{\fa}^i(M))\geq n\text{for all} t\in\nat_0\} and \inf\{\lambda_{\fa R_{\p}}^{\fb R_{\p}}(M_{\p})|\,\p\in {\rm Spec} \, R \text{and} \dim R/ \p\geq n\} are equal, for every finitely generated $R$-module $M$ and for every ideals $\frak a, \frak b$ of $R$ with $\frak b\subseteq \frak a$. This generalizes the Faltings' Annihilator Theorem [G. Faltings, {\it \"Uber die Annulatoren lokaler Kohomologiegruppen}, Arch. Math. {\bf30} (1978) 473-476].Comment: 8 page

Energy-Efficient Resource Allocation for Elastic Optical Networks using Convex Optimization

We propose a two-stage algorithm for energy-efficient resource allocation constrained to QoS and physical requirements in OFDM-based EONs. The first stage deals with routing, grooming and traffic ordering and aims at minimizing amplifier power consumption and number of active transponders. We provide a heuristic procedure which yields an acceptable solution for the complex ILP formulation of the routing and grooming. In the second stage, we optimize transponder configuration including spectrum and transmit power parameters to minimize transponder power consumption. We show how QoS and transponder power consumption are represented by convex expressions and use the results to formulate a convex problem for configuring transponders in which transmit optical power is an optimization variable. Simulation results demonstrate that the power consumption is reduced by 9% when the proposed routing and grooming algorithm is applied to European Cost239 network with aggregate traffic 60 Tbps. It is shown that our convex formulation for transponder parameter assignment is considerably faster than its MINLP counterpart and its ability to optimize transmit optical power improves transponder power consumption by 8% for aggregate traffic 60 Tbps. Furthermore, we investigate the effect of adaptive modulation assignment and transponder capacity on inherent tradeoff between network CAPEX and OPEX.Comment: 28 pages, 11 figures, 4 table

Energy-Efficient Transponder Configuration for FMF-based Elastic Optical Networks

We propose an energy-efficient procedure for transponder configuration in FMF-based elastic optical networks in which quality of service and physical constraints are guaranteed and joint optimization of transmit optical power, temporal, spatial and spectral variables are addressed. We use geometric convexification techniques to provide convex representations for quality of service, transponder power consumption and transponder configuration problem. Simulation results show that our convex formulation is considerably faster than its mixed-integer nonlinear counterpart and its ability to optimize transmit optical power reduces total transponder power consumption up to 32%. We also analyze the effect of mode coupling and number of available modes on power consumption of different network elements.Comment: 4 pages, 4 figures. arXiv admin note: text overlap with arXiv:1705.0689

Analysis and Design of Adaptive OCDMA Passive Optical Networks

OCDMA systems can support multiple classes of service by differentiating code parameters, power level and diversity order. In this paper, we analyze BER performance of a multi-class 1D/2D OCDMA system and propose a new approximation method that can be used to generate accurate estimation of system BER using a simple mathematical form. The proposed approximation provides insight into proper system level analysis, system level design and sensitivity of system performance to the factors such as code parameters, power level and diversity order. Considering code design, code cardinality and system performance constraints, two design problems are defined and their optimal solutions are provided. We then propose an adaptive OCDMA-PON that adaptively shares unused resources of inactive users among active ones to improve upstream system performance. Using the approximated BER expression and defined design problems, two adaptive code allocation algorithms for the adaptive OCDMA-PON are presented and their performances are evaluated by simulation. Simulation results show that the adaptive code allocation algorithms can increase average transmission rate or decrease average optical power consumption of ONUs for dynamic traffic patterns. According to the simulation results, for an adaptive OCDMA-PON with BER value of 1e-7 and user activity probability of 0.5, transmission rate (optical power consumption) can be increased (decreased) by a factor of 2.25 (0.27) compared to fixed code assignment.Comment: 11 pages, 11 figure

Spectrum-Convertible BVWXC Placement in OFDM-based Elastic Optical Networks

Spectrum conversion can improve the performance of OFDM-based Elastic Optical Networks (EONs) by relaxing the continuity constraint and consequently reducing connection request blocking probability during Routing and Spectrum Assignment (RSA) process. We propose three different architectures for including spectrum conversion capability in Bandwidth-Variable Wavelength Cross-Connects (BVWXCs). To compare the capability of the introduced architectures, we develop an analytical method for computing average connection request blocking probability in a spectrum-convertible OFDM-based EON in which all, part or none of the BVWXCs can convert the spectrum. An algorithm for distributing a limited number of Spectrum-Convertible Bandwidth-Variable Wavelength Cross-Connects (SCBVWXCs) in an OFDM-based EON is also proposed. Finally, we use simulation results to evaluate the accuracy of the proposed method for calculating connection request blocking probability and the capability of the introduced algorithm for SCBVWXC placement.Comment: 15 pages, 7 figures, 1 tabl

Thermalization of Mutual Information in Hyperscaling Violating Backgrounds

We study certain features of scaling behaviors of the mutual information during a process of thermalization, more precisely we extend the time scaling behavior of mutual information which has been discussed in \cite{Alishahiha:2014jxa} to time-dependent hyperscaling violating geometries. We use the holographic description of entanglement entropy for two disjoint system consisting of two parallel strips whose widths are much larger than the separation between them. We show that during the thermalization process, the dynamical exponent plays a crucial rule in reading the general time scaling behavior of mutual information (\emph{e.g.,} at the pre-local-equilibration regime). It is shown that the scaling violating parameter can be employed to define an effective dimension.Comment: 24 pages, no figures, conclusion and introduction improved, ref.s added, typos corrected, generalization of arXiv:1406.7677 (thermalization of mutual information part) to time-dependent hyperscaling violating geometries, accepted for publication in JHE

Higher residue pairing on Crystalline local systems

We explain a generalization of the K. Saito higher residue pairing for local system of $p$-adic isocrystals

Serre Intersection Multiplicity Conjecture and Hodge theory

We explain intersection multiplicity defined by J. P. Serre, in terms of the Poincare product in Hodge theory by a modification of the chern character map. We also discuss a formulation of the Euler characteristic via the action of correspondences on the Chow groups of projective varieties, assuming the Grothendieck Standard conjectures over $Q_l$

Variation of Mixed Hodge Structure and Primitive elements

We study the asymptotic behaviour of polarization form in the variation of mixed Hodge structure associated to isolated hypersurface singularities. The contribution characterizes a modification of Grothendieck residue as the polarization on the extended fiber in this case. We also provide a discussion on primitive elements to explain conjugation operator in these variations, already existed in the literature.Comment: This article is a brief of my other article On the mixed Hodge structure associated to isolated hypersurface singularities. Its removal is for its content already existed in the aforementioned paper, with more detail