Cardinality enhancement of spectral/spatial modified double weight code optical code division multi-access system by PIIN suppression

A new two-dimensional (2-D) optical code division multiple access (OCDMA) scheme to increase the achievable system capacity is proposed. The code exhibits good cross-correlation property time and wavelength shift. Performances are analyzed on code size and correlation properties affecting two important system parameters, bit error rate (BER) as a function of cardinality generated and optical power transmission requirement. The proposed system can effectively suppress phase-induced intensity noise (PIIN) and has multi-access interference (MAI) cancellation property. Results in a good agreement indicate that 2-D modified double weight (MDW) offers 163.7% and 336.2% larger cardinality compare to 2-D perfect difference code (PDC) and 2-D modified quadratic congruence (MQC) code. By increasing spatial code (N) and keeps similar code length system performance can be further optimized. 2-D MDW (M = 45, N = 18) accommodates 252.2% and 18.3% cardinality increment and low effective transmitted power (P_sr) at −17.9 dBm, compare to 2-D MDW (M = 247, N = 3) and (M = 84, N = 9) at 10⁻⁹ BER error floor. The architecture of the spectral/spatial MDW OCDMA system with property of MAI cancellation is presented.     

On (3,3)-Homogeneous Greechie Orthomodular Posets

We describe (3,3)-homogeneous orthomodular posets for some cardinality of their sets of atoms. We examine a state space and a set of two-valued states of such logics. Particular homogeneous OMPs with exactly k pure states (k = 1,...,7, 10,11) have been constructed.     

Cardinality enrichment of flexible cross correlation (FCC) code for SAC-OCDMA system by alleviation interference scheme (AIS)

In this paper, we propose an alleviation interference scheme (AIS) for spectral amplitude coding (SAC) – optical code division multiple access (OCDMA) coding system approaches. The AIS SAC-OCDMA systems is demonstrated by utilizing the new flexible cross correlation (FCC) code. The FCC code has advantages, such as flexibility in-phase cross-correlation at any given number of users and weights, as well as effectively reduces the impacts of phase-induced intensity noise (PIIN) and has the multiple-access interference (MAI) cancelation property. The results indicated good performance whereas the FCC (W = 4, K = 150) AIS SAC-OCDMA coding system offers 66%, 172%, 650% and 900% percentage of cardinality enrichments as a contrast to DCS (W = 4, K = 90), MDW (W = 4, K = 55), MFH (W = 4, K = 20) and Hadamard (W = 8, K = 15) codes, respectively. Finally, the FCC AIS SAC-OCDMA coding system has low effective receive power Psr = −21 dBm which is expected to be more significant for future SAC-OCDMA coding systems without requiring any amplification at the receiving plant.     

Solving the undirected feedback vertex set problem by local search

An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, in which case a feedback vertex set (FVS) is a set of vertices intersecting with each of these cycles. Constructing a FVS of cardinality approaching the global minimum value is an optimization problem in the nondeterministic polynomial-complete complexity class, and therefore it might be extremely difficult for some large graph instances. In this paper we develop a simulated annealing local search algorithm for the undirected FVS problem by adapting the heuristic procedure of Galinier et al. [P. Galinier, E. Lemamou, M.W. Bouzidi, J. Heuristics 19, 797 (2013)], which worked for the directed FVS problem. By defining an order for the vertices outside the FVS, we replace the global cycle constraints by a set of local vertex constraints on this order. Under these local constraints the cardinality of the focal FVS is then gradually reduced by the simulated annealing dynamical process. We test this heuristic algorithm on large instances of Erdös-Rényi random graph and regular random graph, and find that this algorithm is comparable in performance to the belief propagation-guided decimation algorithm.     

Construction of optimal 2D variable-weight optical orthogonal codes for high-speed OCDMA networks

A new construction method of two-dimensional （2D） variable-weight optical orthogonal codes （VWOOCs） is proposed for high-speed optical code-division multiple-access （OCDMA） networks supporting multiple qualities of services （QoS）. The proposed codes have at most one-pulse per wavelength （AM-OPPW） property. An upper bound of the codeword cardinality of the 2D VWOOCs with AM-OPPW property is derived. It is then shown that the constructed codes have ideal correlation properties and optimal cardinality. Moreover, the code length and the bit-error-rate （BER） performance of the proposed codes are compared with those of the codes proposed previously.     

Symmetric chain partitions of orthocomplemented posets

It is shown that any orthocomplemented posetP of finite width admits a chain partition of cardinality 2[2/3 width(P)] which is symmetrical with respect to the orthocomplement. This cardinality is the best possible.     

Two-Party Privacy-Preserving Set Intersection with FHE

A two-party private set intersection allows two parties, the client and the server, to compute an intersection over their private sets, without revealing any information beyond the intersecting elements. We present a novel private set intersection protocol based on Shuhong Gao’s fully homomorphic encryption scheme and prove the security of the protocol in the semi-honest model. We also present a variant of the protocol which is a completely novel construction for computing the intersection based on Bloom filter and fully homomorphic encryption, and the protocol’s complexity is independent of the set size of the client. The security of the protocols relies on the learning with errors and ring learning with error problems. Furthermore, in the cloud with malicious adversaries, the computation of the private set intersection can be outsourced to the cloud service provider without revealing any private information.     

A new family of two-dimensional triple-codeweight asymmetric optical orthogonal code for OCDMA networks

A new generation algorithm of two-dimensional triple-codeweight asymmetric optical orthogonal codes for optical code division multiple access （OCDMA） networks is proposed. The code cardinality is obtained and the error-probability performance for corresponding OCDMA system is analyzed. The codes with two constraints （i.e., auto- and cross-correlation properties） being unequal are taken into account. On the premise of fixed system resources, the code of the error-probability performance, it is shown cardinality can be significantly improved. By analysis that the codes with different parameters have different performances. Therefore, this type of codes can be applied to support diverse quality of service （QoS） and satisfy the quality requirement of different multimedia or distinct users, and simultaneously make the better use of bandwidth resources in oDtical networks.     

Geometric quantization of symplectic manifolds with respect to reducible non-negative polarizations

The leafwise complex of a reducible non-negative polarization with values in the prequantum bundle on a prequantizable symplectic manifold is studied. The cohomology groups of this complex is shown to vanish in rank less than the rank of the real part of the non-negative polarization. The Bohr-Sommerfeld set for a reducible non-negative polarization is defined. A factorization theorem is proved for these reducible non-negative polarizations. For compact symplectic manifolds, it is shown that the above complex has finite dimensional cohomology groups, more-over a Lefschetz fixed point theorem and an index theorem for these non-elliptic complexes is proved. As a corollary of the index theorem, we deduce that the cardinality of the Bohr-Sommerfeld set for any reducible real polarization on a compact symplectic manifold is determined by the volume and the dimension of the manifold. Supported in part by NSF grant DMS-93-09653, while the author was visiting University of California Berkeley.     

Quantum sets and clifford algebras

The mathematical language presently used for quantum physics is a high-level language. As a lowest-level or basic language I construct a quantum set theory in three stages: (1) Classical set theory, formulated as a Clifford algebra of “S numbers” generated by a single monadic operation, “bracing,” Br = {…}. (2) Indefinite set theory, a modification of set theory dealing with the modal logical concept of possibility. (3) Quantum set theory. The quantum set is constructed from the null set by the familiar quantum techniques of tensor product and antisymmetrization. There are both a Clifford and a Grassmann algebra with sets as basis elements. Rank and cardinality operators are analogous to Schroedinger coordinates of the theory, in that they are multiplication or “Q-type” operators. “P-type” operators analogous to Schroedinger momenta, in that they transform theQ-type quantities, are bracing (Br), Clifford multiplication by a setX, and the creator ofX, represented by Grassmann multiplicationc(X) by the setX. Br and its adjoint Br* form a Bose-Einstein canonical pair, andc(X) and its adjointc(X)* form a Fermi-Dirac or anticanonical pair. Many coefficient number systems can be employed in this quantization. I use the integers for a discrete quantum theory, with the usual complex quantum theory as limit. Quantum set theory may be applied to a quantum time space and a quantum automaton. This material is based upon work supported in part by NSF Grant No. PHY8007921.     

Ring-based PON supporting multiple optical private networks using OCDMA technique

This work is a novel attempt to provide local communications for multiple optical private networks (PNs) within ring-based passive optical network (PON). In order to improve network throughput performance, PNs traffic is decentralized from PON traffic let no extra traffic management into optical line terminal (OLT). To achieve multiple secure optical private networking over ring-based PON layout, optical code division multiple access (OCDMA) technique is applied. This technique leads to interconnect optical network units (ONUs) in the same PN sharing the same codeword while other PNs benefiting from different codewords. This scheme can be used in access networks to establish discrete communications between different sites in an enterprise or a university campus or even a residential accommodation. The proposed network architecture is then set up and its bit error rate performance is experimentally demonstrated. Finally, the network scalability and throughput performance of the proposed scheme are analyzed.     

Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist

A partition of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite natural number n > 2, the probability space (Ω,p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation.     

Deformation of Towers of Algebras and Quantized Intersection Cardinality Functions

The inductive limit of a tower of separable algebras is unchanged, up to isomorphism, by consistent deformations but the inductive limit of a corresponding tower of modules may be nontrivially deformed, thereby quantizing the limit module. In the case of the inductive limit of the complex group algebras of the symmetric groups and their deformations, the Hecke algebras, this quantization preserves properties of the finite case which disappear in the absence of quantization.     

Quality of Service Control Based on Virtual Private Network Services in a Wide Area Gigabit Ethernet Optical Test Bed

Abstract

We report an experimental investigation about the Virtual Private LAN Service technique to guarantee the quality of service in the metro/core network and also in the presence of access bandwidth bottleneck. We also show how the virtual private network can be set up for answering to a user request in a very fast way. The tests were performed in a GMPLS test bed with GbE core routers linked with long (tens of kilometers) GbE G.652 fiber links.     

Automorphism Groups of Orthomodular Lattices Obtained from Quadratic Spaces

We study the automorphism group of some orthomodular lattices, obtained from a quadratic space over a field K. We show how this group is linked to the semi-orthogonal group and with the group of all similarity transformations of the quadratic space. When the field K is finite, the cardinality of the automorphism group is given. AMS subject classification (1991): 06C15, 15A63, 20D45.     

Finite-space Lyapunov exponents and pseudochaos

We propose a definition of finite-space Lyapunov exponent. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by showing that, for large classes of chaotic maps, the corresponding finite-space Lyapunov exponent approaches the Lyapunov exponent of a chaotic map when M-->infinity, where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has pseudochaos if its finite-space Lyapunov exponent tends to a positive number (or to +infinity), when M-->infinity.     

Secure key from bound entanglement

We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states that have less distillable private keys than the entanglement cost of the state. In general, the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.     

Only Countable Reichenbachian Common Cause Systems Exist

In this paper we give a positive answer to a problem posed by Hofer-Szabó and Rédei (Int. J. Theor. Phys. 43:1819–1826, 2004) regarding the existence of infinite Reichenbachian common cause systems (RCCSs). An example of a countably infinite RCCS is presented. It is also determined that no RCCSs of greater cardinality exist.     

Quantum Private Comparison of Equality Based on Five-Particle Cluster State

A protocol for quantum private comparison of equality (QPCE) is proposed based on five-particle cluster state with the help of a semi-honest third party (TP). In our protocol, TP is allowed to misbehave on its own but can not conspire with either of two parties. Compared with most two-user QPCE protocols, our protocol not only can compare two groups of private information (each group has two users) in one execution, but also compare just two private information. Compared with the multi-user QPCE protocol proposed, our protocol is safer with more reasonable assumptions of TP. The qubit efficiency is computed and analyzed. Our protocol can also be generalized to the case of 2N participants with one TP. The 2N-participant protocol can compare two groups (each group has N private information) in one execution or just N private information.