71,671 research outputs found
Unextendible Product Basis for Fermionic Systems
We discuss the concept of unextendible product basis (UPB) and generalized
UPB for fermionic systems, using Slater determinants as an analogue of product
states, in the antisymmetric subspace \wedge^ N \bC^M. We construct an
explicit example of generalized fermionic unextendible product basis (FUPB) of
minimum cardinality for any . We also show that any
bipartite antisymmetric space \wedge^ 2 \bC^M of codimension two is spanned
by Slater determinants, and the spaces of higher codimension may not be spanned
by Slater determinants. Furthermore, we construct an example of complex FUPB of
with minimum cardinality . In contrast, we show that a real FUPB
does not exist for . Finally we provide a systematic construction for
FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.Comment: 17 pages, no figure. Comments are welcom
Optimal random search, fractional dynamics and fractional calculus
What is the most efficient search strategy for the random located target
sites subject to the physical and biological constraints? Previous results
suggested the L\'evy flight is the best option to characterize this optimal
problem, however, which ignores the understanding and learning abilities of the
searcher agents. In the paper we propose the Continuous Time Random Walk (CTRW)
optimal search framework and find the optimum for both of search length's and
waiting time's distributions. Based on fractional calculus technique, we
further derive its master equation to show the mechanism of such complex
fractional dynamics. Numerous simulations are provided to illustrate the
non-destructive and destructive cases.Comment: 12 pages, 7 figure
Delay-Energy lower bound on Two-Way Relay Wireless Network Coding
Network coding is a novel solution that significantly improve the throughput
and energy consumed of wireless networks by mixing traffic flows through
algebraic operations. In conventional network coding scheme, a packet has to
wait for packets from other sources to be coded before transmitting. The
wait-and-code scheme will naturally result in packet loss rate in a finite
buffer. We will propose Enhanced Network Coding (ENC), an extension to ONC in
continuous time domain.
In ENC, the relay transmits both coded and uncoded packets to reduce delay.
In exchange, more energy is consumed in transmitting uncoded packets. ENC is a
practical algorithm to achieve minimal average delay and zero packet-loss rate
under given energy constraint. The system model for ENC on a general renewal
process queuing is presented. In particular, we will show that there exists a
fundamental trade-off between average delay and energy. We will also present
the analytic result of lower bound for this trade-off curve, which can be
achieved by ENC
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