Synchrony with shunting inhibition in a feedforward inhibitory network Recent experiments have shown that GABA A receptor mediated inhibition in adult hippocampus is shunting rather than hyperpolarizing. Simulation studies of realistic interneuron networks with strong shunting inhibition have been demonstrated to exhibit robust gamma band (20-80 Hz) synchrony in the presence of heterogeneity in the intrinsic firing rates of individual neurons in the network. In order to begin to understand how shunting can contribute to network synchrony in the presence of heterogeneity, we develop a general theoretical framework using spike time response curves (STRC's) to study patterns of synchrony in a simple network of two unidirectionally coupled interneurons (UCI network) interacting through a shunting synapse in the presence of heterogeneity. We derive an approximate discrete map to analyze the dynamics of synchronous states in the UCI network by taking into account the nonlinear contributions of the higher order STRC terms. We show how the approximate discrete map can be used to successfully predict the domain of synchronous 1:1 phase locked state in the UCI network. The discrete map also allows us to determine the conditions under which the two interneurons can exhibit in-phase synchrony. We conclude by demonstrating how the information from the study of the discrete map for the dynamics of the UCI network can give us valuable insight into the degree of synchrony in a larger feedforward network of heterogeneous interneurons. Synchronous rhythms in the brain, in particular gamma rhythms are known to constitute a fundamental mechanism for cognitive tasks such as object recognition (Mima et al. 2001; Baudry and Bertrand 1999) , associative learning (Gruber et al. 2001 (Gruber et al. , 2002 and the processing of sensory information in the brain (Engel and Singer 2001; Aoki 1999) . A number of in-vitro slice experiments have demonstrated that fast inhibitory response mediated by GABA A receptors are both necessary and sufficient for the generation of sustained gamma-band oscillations in the hippocampus (Whittington et al. 1995; Fisahn et al. 1998; LeBeau et al. 2002; Mann et al. 2005) . Early theoretical work by Wang and Rinzel (1992) , demonstrating the ability for reciprocally connected interneurons to exhibit synchronous rhythms, provided a mechanistic framework for synchrony exhibited by purely inhibitory neuronal network. In the subsequent years there have been a number of theoretical and simulation studies of synchrony in networks of coupled interneurons (vanVreeswijk et al. 1994; Wang and Buzsaki 1996; Ernst et al. 1995; White et al. 1998; Chow et al. 1998 ). The primary conclusion from these studies was that while homogeneous networks of inhibitory coupled neurons can exhibit synchrony, it was extremely sensitive to heterogeneity in the network parameters. Most of the earlier theoretical work focused on hyperpolarizing effects of GABA A mediated fast inhibition. However recent experimental work by Bartos et.al., has demonstrated that GABA A mediated inhibition in hippocampal slices of adult mammalian brains, is fast and shunting (Bartos et al. 2002; Vida et al. 2006) . Through simulation studies on a realistic network model of coupled interneurons, the authors have also demonstrated that shunting enhances robust gamma-band synchrony in the network even in the presence of moderately high heterogeneity (Bartoset et al. 2007) . However due to the inherent complexity of the realistic network considered by Bartos et.al, (a large network comprising of 200 interneurons, electrical coupling among neighboring pair of interneurons, the presence of synaptic propagation delay, fast synaptic decay time, strong synaptic conductance) it has been difficult to elucidate the contribution of shunting to the enhancement of synchrony of the network in the gamma-band. Infact recent theoretical work by Jeong and Gutkin (2007) suggests that shunting may enhance stable asynchronous states in the network of coupled interneurons. However the authors note that the observed difference between their results and those obtained by Bartos et.al., may lie in the different regimes of synaptic coupling considered and the lack of heterogeneity in the intrinsic firing rates of the coupled neurons.. Here, we investigate whether the analytical framework of spike time response curves (STRCs) can be used to study synchronous state of 1:1 phase locking between two unidirectionally coupled neurons (UCI network) interacting through a strong shunting synapse in the presence of heterogeneity (Talathi et al. 2009 ). We begin by demonstrating that synaptic input through shunting inhibition to a neuron periodically firing in the gamma frequency band persists for 3 consecutive firing cycles as opposed to the case for neuron receiving strong synaptic input through a hyperpolarizing synapse. We then develop an analytical framework to approximate the dynamics of 1:1 synchronous state in the UCI network through a discrete map that takes into account the higher order STRC contributions. We show that in the limit of zero higher order STRC contributions the discrete map reduces to the well-known approximation for synchrony between two neurons coupled through a hyperpolarizing inhibitory synapse (Ermentrout 1996; Acker et al. 2004; Talathi et al. 2008) . We then use the discrete map to determine the conditions under which in-phase synchrony can be observed in this network. We show that synaptic delays play an important role in the generation of inphase synchrony between the two coupled interneurons interacting through a shunting synapse. In the spirit of White et al. (1998) , we conclude by demonstrating that analysis of smaller networks can be useful in understanding larger network dynamics and may provide more insight into the results obtained by Bartoset et al. (2007) for a more biologically realistic networks. In this work we have presented a general mathematical framework to analyze patterns of synchrony in a simple feed-forward network of heterogeneously firing neurons interacting through a shunting synapse. Our work is motivated from the recent experimental findings by Bartoset et al. (2007) , demonstrating the ability for a realistic interneuronal network to exhibit robust gamma-band synchrony through shunting synapse in the presence of heterogeneity. Our work is an extension of the theoretical analysis by Jeong and Gutkin (2007) in that we consider the more general case of two neurons coupled through a strong shunting synapse in the presence of heterogeneity. By considering a more simpler situation of uni-directionally coupled neurons, we demonstrate that the results of Jeong and Gutkin pretty much hold true even in the presence of strong-shunting synapse with heterogeneity. In absence of delays in the synaptic transmission, both slow and fast shunting fail to exhibit inphase synchrony between unidirectionally coupled interneurons. The applicability of our methodology as presented in this paper to study patterns of synchrony emerging in a more realistic neuronal network such as considered by Bartoset et al. (2007) remains a topic of future investigation.. The mathematical framework presented in this work is based on the technique of phase reduction which is commonly employed in the study of pulse coupled oscillators (Winfree 2001; Murray 1993) . The technique involves determining the phase response curve (PRC) for an oscillator that quantifies how the oscillator responds to a perturbation through a pulsatile input. The PRC for a neuron receiving synaptic perturbations is measured in terms of time rather than phase (Acker et al. 2004 ) and is referred to as the spike time response curve (STRC). The STRC's provide a natural experimental framework to study the perturbation effects of synaptic inputs on the firing times of a neuron without the requirement of a detailed biophysical model to mimic the neuronal dynamics. We want to emphasize this point by noting that experimental neuroscientists interested in network synchrony do not necessarily know all the ion channels that comprise a neuronal membrane. However it is relatively easy to stimulate a neuron and measure the response time of the neuronal firing and thereby create an experimental log of the effect of synaptic perturbation on a regularly spiking neuron. Once STRC's are determined as described above in the open loop setting, the framework we presented in this work can be used to analyze local synchrony between coupled neurons and in the special case of feed-forward network of inhibitory neurons, make predictions about network synchrony.. We began by demonstrating that STRC's are in general a function of synaptic parameters and for a given level of synaptic strength and synaptic kinetics, the effect of synaptic input varies depending on the form of synaptic inhibition, i.e., hyperpolarizing vs. shunting. For hyperpolarizing synapse, the dominant effect of synaptic perturbation is on the firing cycle that receives the perturbation. However for shunting inhibition, the perturbation effect persists beyond the cycle in which the neuron receives the synaptic perturbation. We found that the analytical technique of re-normalization and re-scaling allowed us to correctly account for the contributions from the higher order STRC terms to the instantaneous firing period of a neuron receiving synaptic input in multiple successive firing cycles. The main advantage of this technique is that it does not require the neuron to approach its intrinsic period of oscillation before receiving the next synaptic perturbation. As a result this technique allowed us to approximate the network dynamics of two heterogeneously firing neurons coupled through a shunting synapse through a discrete map that has the ability to predict the stability of patterns of synchrony in the network. The discrete map also allowed us to determine the conditions under which a larger feed-forward network of heterogeneously firing interneurons can exhibit inphase synchrony. Although in this work we restrict our analysis to the study of feedforward networks, the analytical framework we developed here is equally applicable to study patterns of synchrony generated by a pair of mutually coupled neurons (Talathi et al. 2009 ). Discrete map analysis for mutually coupled neurons is in particular more challenging. For a given level of heterogeneity, one has to determine STRC's for both neurons in the coupled network (each neuron firing with its own intrinsic period) in order to obtain a discrete map similar to Eq. (10). However once the STRC's are known, one can follow the methodology presented in this work to determine a nonlinear discrete map, stability of the fixed point solution of which can then predict the existence of 1:1 synchronous states (Talathi et al. 2009 ).. While the methodology that we present in this work enables one to carefully design neuronal networks that can exhibit complete synchrony, the question remains whether such an artificial construction of a neuronal network has any biological relevance. In particular is there a biological mechanism for altering the effective delay in signal propagation between coupled neurons? One particularly relevant pathophysiological scenario that leads to a hypersynchrony of brain networks is the mossy fiber sprouting, which triggers a synaptic reorganization in the dentate gyrus of patients and animal models of temporal lobe epilepsy (Dudek and Shao 2004) . The axons of the dentate gyrus excitatory granule cells, develop collaterals that grow into the dentate gyrus molecular layer. A commonly acceptable hypothesis for seizure generation in patients with temporal lobe epilepsy is that the mossy fiber sprouting trigger hypersynchrony by forming recurrent excitatory connections between the granule cells. It may well be that the modification in the axonal fibers synapsing onto the granule cell bodies may alter the effective delay in the propagation of recurrent excitatory signal and by the mechanisms we propose in this work, trigger a hypersynchronous brain state that eventually leads to the generation of a spontaneous epileptic seizure. More recently there has been a growing interest in controlling the geometry of cell cultures in multielectrode array systems to utilize specially constructed neuronal circuits for various computational tasks such as logic operations (Wolf and Geisel 2008) . In the same spirit one can envision the construction of a specialized neuronal circuitry that is tuned to oscillate in synchrony. Such a neuronal circuitry can then be utilized to understand the mechanisms and function of neural synchrony in computation such as the binding problem (Sejnowski 1986 ). More over different pharmacological drugs can be devised to alter the effective delay in synaptic propagation to break the network synchrony and there by provide an effective control over runaway hypersynchronous brain states that trigger epileptic seizures.. In conclusion, we found that in the feed-forward network of interneurons coupled through a strong shunting synapse, synaptic delays play a critical role in the generation of synchronous oscillations. Another important criteria for the observation of synchrony in a large feed-forward network is the the requirement for local pair of interneurons to be within the Arnold's tongue for 1:1 synchrony. The ability for the framework developed here in determining the synchronizability of a realistic interneuronal network in the presence of heterogeneity as those considered by Bartos et.al., remains a topic of future investigation.

B O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


SoRoute:

a

reliable

and

effective

social-based

routing

in

cognitive

radio

ad

hoc

networks

A

cognitive

radio

ad

hoc

network

(CRAHN)

can

be

considered

as

a

special

delay

tolerant

network

(DTN)

that

is

composed

of

mobile

secondary

users

(SUs)

with

social

characteristics.

Given

intermittent

connectivity

and

spectrum

availability,

it

is

a

challenging

issue

regarding

how

to

transmit

messages

between

SUs

in

a

reliable

and

effective

way

in

CRAHNs.

To

tackle

this

challenge,

we

propose

a

social-aware

opportunistic

routing

and

relay

selection

scheme,

called

SoRoute,

which

first

predicts

the

link

reliability

based

on

a

new

social-relationship-aware

mobility

model

and

then

fuses

the

relationships

of

SUs

to

make

a

routing

and

relay

decision.

In

our

design,

different

prediction

schemes

are

employed

for

the

nodes

with

different

relationships.

A

message

is

forwarded

to

the

relay

node

with

the

largest

encounter

probability

with

the

destination.

The

evaluation

results

demonstrate

that

our

social-based

opportunistic

routing

scheme

significantly

improves

the

performance

compared

to

the

existing

routing

schemes

such

as

Direct

Delivery,

First

Contact,

MaxProp,

and

Prophet.

A

cognitive

radio

(CR)

is

a

promising

technology

to

address

the

spectrum

scarcity

problem

and

improve

spectrum

utilization,

which

enables

secondary

users

(SUs)

opportunistically

access

the

vacant

spectrum

bands

allocated

to

primary

users

(PUs)

Due

to

the

specific

characteristics

of

CR,

it

has

broad

application

prospects.

For

example,

CR

technology

can

be

combined

with

mobile

ad

hoc

networks,

which

is

called

cognitive

radio

ad

hoc

networks

(CRAHNs)

in

which

wireless

devices

can

dynamically

establish

networks

using

the

vacant

spectrum

bands

allocated

to

PUs

without

the

need

of

fixed

infrastructures.

However,

the

distinct

characteristics

of

CRAHNs,

such

as

the

mobility

of

nodes

and

the

limitation

of

spectrum,

result

in

intermittent

connectivity

in

such

networks.

The

lack

of

a

sustainable

end-to-end

path

makes

CRAHNs

appear

to

be

delay

tolerant

networks

(DTNs)

All

of

the

DTN

routing

methods

share

a

similar

characteristic,

the

'store-carry-forward'

fashion.

That

means

a

DTN

node

can

store

and

carry

the

data

until

it

encounters

a

suitable

node.

From

a

routing

perspective,

a

link

is

considered

to

be

reliable

if

the

link

duration

time

is

longer

than

the

time

required

for

transmitting

data.

It

is

an

unreliable

link

otherwise.

An

unreliable

link

may

be

broken

frequently.

When

any

link

of

a

path

fails,

this

path

has

to

be

either

repaired

by

finding

another

link

or

replaced

entirely

with

a

new

path.

These

rerouting

operations

waste

the

scarce

radio

resource

and

battery

power,

and

rerouting

delay

may

also

affect

quality

of

service

(QoS)

and

degrade

network

performances

As

a

result,

the

reliability

of

a

link

is

an

important

criterion

of

measuring

whether

a

link

can

be

used

to

forward

a

message.

Furthermore,

due

to

the

limitation

of

spectrum

availability

and

node

mobility,

routing

in

CRAHNs

may

incur

a

long

delay.

Thus,

it

is

a

challenging

problem

how

to

transmit

messages

reliably

and

efficiently

in

CRAHNs..

Most

of

the

existing

DTN

routing

schemes

are

based

on

classic

ad

hoc

networks,

ignoring

the

spectrum

availability.

However,

routing

in

CRAHNs

should

take

into

consideration

not

only

the

mobility

of

nodes

but

also

the

spectrum

availability

which

is

under

the

condition

that

SUs

can

not

generate

interference

to

PUs.

In

addition,

many

previous

works

on

routing

in

ad

hoc

networks

assumed

that

messages

would

be

forwarded

completely

once

two

nodes

encounter

with

each

other

Obviously,

this

assumption

is

unreasonable

when

message

size

is

large

and

mobility

is

high.

Based

on

the

analysis

above,

a

link

reliability

prediction

scheme

is

necessary

in

CRAHNs.

Mobile

SUs

have

social

relationships.

Portable

devices,

such

as

smart

phones

or

ipads,

are

always

carried

by

human

beings.

Therefore,

the

mobility

pattern

of

these

nodes

corresponds

to

that

of

their

users.

Empirical

observations

indicate

there

exists

certain

social

relationships

between

different

people,

and

people

of

different

relationships

have

different

social

behaviors.

For

example,

friends

stay

together

longer

than

strangers,

and

colleagues

or

classmates

meet

more

frequently

than

distant

relations.

A

link

reliability

can

be

better

predicted

and

a

routing

decision

can

be

better

made

by

exploring

these

social

relationships.

A

few

of

existing

works

considers

the

concept

of

social

networks

in

DTN

routing.

However,

most

of

these

studies

are

made

from

the

view

of

social

characteristics

such

as

community

and

centrality.

Few

of

them

model

and

conduct

qualitative

analysis

on

the

link

duration

and

encounter

probabilities

of

SUs

based

on

the

different

relationships

of

the

nodes..

In

this

paper,

we

propose

a

novel

opportunistic

routing

and

relay

selection

scheme,

called

SoRoute,

which

forwards

the

messages

based

on

the

social

relationships

between

the

nodes

in

a

reliable

and

efficient

way.

The

main

contributions

of

this

paper

are

summarized

as

follows:.

A

new

mobility

model

is

proposed,

which

can

represent

the

mobility

patterns

of

nodes

with

the

real-world

social

relationships..

Based

on

this

model,

a

link

reliability

metric

and

a

prediction

algorithm

are

derived

for

the

SUs

with

different

relationships,

taking

into

account

SUs'

transmission

range

limitation

and

interference

with

PUs..

We

propose

a

routing

and

relay

selection

protocol

based

on

the

social-aware

link

reliability..

We

demonstrate

the

proposed

social-based

opportunistic

routing

scheme

that

significantly

improves

the

performance

compared

to

the

existing

routing

schemes

such

as

Direct

Delivery,

First

Contact,

MaxProp,

and

Prophet..

To

the

best

of

our

knowledge,

this

is

the

first

work

to

combine

the

concept

of

social

relationships

with

the

prediction

of

link

reliability

for

routing

and

relay

selection.

The

rest

of

this

paper

is

organized

as

follows.

Section

presents

the

related

work.

In

section

network

model

and

mobility

model

are

presented.

Section

gives

a

brief

introduction

of

the

social

relationships

between

human

beings.

The

link

reliability

prediction

algorithm

is

given

in

section

The

social-based

opportunistic

routing

scheme

is

described

in

section

In

section

we

demonstrate

the

validity

of

our

link

reliability

prediction

algorithm.

The

performance

of

the

proposed

routing

scheme

is

also

evaluated.

Section

gives

the

conclusions.

In

this

paper,

we

propose

a

social-based

routing

scheme

for

CRAHNs.

The

proposed

routing

scheme

utilizes

the

social

relationships

between

people

to

select

relays

in

a

reliable

and

effective

way.

The

simulation

results

show

that

our

routing

scheme

achieves

a

much

better

performance

in

terms

of

packet

loss

rate

and

overhead

ratio

than

the

existing

routing

schemes

such

as

Direct

Delivery,

First

Contact,

MaxProp,

and

Prophet.

Our

future

work

involves

improving

the

mobility

model

and

validate

it

using

more

realistic

data.

The

existing

DTN

routing

schemes

can

be

categorized

into

two

classes,

flooding

and

forwarding

A

flooding

approach

is

based

on

the

principle

of

forwarding

messages

to

all

the

neighboring

nodes.

Due

to

the

limitation

of

bandwidth

and

buffer

space,

the

flooding

approach

performs

poorly

in

many

situations.

A

forwarding

strategy

uses

certain

knowledge

about

the

network

to

select

a

best

path

to

the

destination.

Cheng

et

al.

propose

a

location-based

routing

method

for

DTN

which

can

estimate

the

minimum

distance

between

the

source

and

destination,

then

messages

are

transmitted

through

the

best

path.

In

the

weight

is

assigned

to

each

node,

which

represents

the

suitability

of

the

node

to

deliver

messages

to

a

given

destination.

This

algorithm

only

delivers

messages

to

the

relay

which

has

a

better

weight

than

the

current

node,

thus

it

is

called

gradient

routing

strategy.

Srinivasa

and

Krishnamurthy

use

'conditional

inter-meeting

time'

as

a

metric

to

estimate

the

best

path

towards

the

destination,

which

can

achieve

a

high

delivery

rate

and

a

short

end-to-end

delay..

In

addition,

social-based

routing

algorithms

have

been

proposed

to

exploit

certain

social

characteristics

in

DTN

Hui

et

al.

propose

a

forwarding

strategy

named

Bubble

Rap,

which

focuses

on

the

community

and

centrality

of

the

nodes.

It

delivers

messages

by

using

the

global

ranking

and

the

local

ranking.

In

a

SimBet

Routing

is

proposed

which

exploits

the

exchange

of

pre-estimated

betweenness

centrality

metrics

and

locally

determined

social

similarity

to

the

destination

node.

Wang

et

al.

exploit

the

spatial

locality,

spatial

regularity,

and

activity

heterogeneity

of

human

mobility

to

select

relays.

Wang

et

al.

summarize

the

behavioral

traits

of

human

beings

employed

by

existing

PSN

routing

schemes

and

give

a

survey

on

PSN

routing

techniques.

Bulut

and

Szymanski

introduce

a

new

metric

for

detecting

the

quality

of

friendships,

and

then

the

temporally

differentiated

friendships

are

used

to

make

the

forwarding

decisions

of

messages.

Gao

et

al.

study

multicast

in

DTNs

from

the

social

network

perspective,

in

which

relay

selections

for

multicast

is

formulated

as

a

unified

knapsack

problem

by

exploiting

node

centrality

and

social

community

structures..

However,

of

the

above

works

considered

CRAHNs.

In

CRNs,

SUs

can

opportunistically

access

the

vacant

bands

allocated

to

PUs

Huang

et

al.

study

a

social-based

routing

in

intermittently

connected

mobile

cognitive

radio

network,

but

it

did

not

consider

the

link

reliability

in

message

forwarding.

Therefore,

a

link

duration

prediction

scheme

is

needed

to

analyze

the

reliability

of

a

link.

The

existing

work

on

link

reliability

prediction

is

limited

Han

et

al.

proposed

an

algorithm,

named

LBRP,

which

can

predict

link

availability

over

a

short

time

by

a

rough

estimation

of

the

distance

between

two

nodes.

However,

LBRP

is

based

on

the

random

walk

mobility

model,

which

is

too

simple

to

reflect

the

mobility

in

real

world.

In

a

prediction-based

link

reliability

estimation

algorithm

and

its

enhanced

version

were

developed.

These

two

algorithms

try

to

predict

the

probability

of

an

active

link

between

two

nodes

being

continuously

available

for

a

certain

period

of

time.

However,

they

are

based

on

statistics

and

can

only

represent

the

general

tendency

of

the

link

availability.

In

addition,

a

link

prediction

scheme

is

proposed

for

CR-MANETs

which

is

aware

of

the

interference

to

primary

users.

However,

this

link

prediction

scheme

is

only

based

on

the

current

node

movement

and

cannot

accurately

calculate

the

link

reliability.

To

the

best

of

our

knowledge,

there

is

no

link

reliability

prediction

scheme

available

in

literature

that

takes

into

account

the

social

characteristics

and

mobility

of

nodes,

as

well

as

interference

to

the

PUs.

O O O O O O B O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Optimal Multiple Surface Segmentation With Shape and Context Priors Abstract-Segmentation of multiple surfaces in medical images is a challenging problem, further complicated by the frequent presence of weak boundary evidence, large object deformations, and mutual influence between adjacent objects. This paper reports a novel approach to multi-object segmentation that incorporates both shape and context prior knowledge in a 3-D graph-theoretic framework to help overcome the stated challenges. We employ an arc-based graph representation to incorporate a wide spectrum of prior information through pair-wise energy terms. In particular, a shape-prior term is used to penalize local shape changes and a context-prior term is used to penalize local surface-distance changes from a model of the expected shape and surface distances, respectively. The globally optimal solution for multiple surfaces is obtained by computing a maximum flow in a low-order polynomial time. The proposed method was validated on intraretinal layer segmentation of optical coherence tomography images and demonstrated statistically significant improvement of segmentation accuracy compared to our earlier graph-search method that was not utilizing shape and context priors. The mean unsigned surface positioning errors obtained by the conventional graph-search approach ( m) was improved to m when employing our new method with shape and context priors. O VER the recent years, automated segmentation of medical images became an important tool contributing to medical diagnosis and treatment planning. Despite all the invested effort, accurate segmentation of organs and other structures of interest remains a challenging problem. The main difficulty lies in the following aspects. First, target objects in medical image data often lack strong boundaries. Second, target objects are often surrounded by adjacent tissues with similar intensity profiles. Furthermore, there are often many objects lying in a small region with contextual mutual influence between each other [1] , [2] .. To resolve these problems, incorporating prior knowledge in the solution process plays an important role. We report a novel algorithm for simultaneous detection of multiple surfaces using both shape and context prior information. Our method is based on our previously reported graph search framework-a globally optimal surface detection method proposed in [3] - [5] , which has been successfully applied to a variety of medical imaging applications (e.g., [6] - [9] ). The basic idea is to formulate the image segmentation problem as an energy optimization problem, which can be solved by a graph-based method. The original graph search formulation [3] , [4] only used weighted nodes in the graph to represent the desired segmentation properties, which limited the ability to incorporate a broader variety of a priori knowledge. In this work, we propose a novel extension to this graph search method. Two additional pair-wise terms are added to the energy function, which encode the shape and context prior information using a set of convex functions. For optimization, new pair-wise terms are enforced by adding specific weighted arcs in the graph. A globally optimal solution is computed by solving a single maximum flow problem in the graph with the solution defining the optimally segmented surfaces.. The remainder of the paper is organized as follows. Section II reviews the related work on image segmentation. Section III presents how to incorporate both shape and context information in the graph search framework using an arc-weighted graph representation. In Section IV, our approach is applied to intraretinal layer segmentation in optical coherence tomography (OCT) images and Section VII discusses the novelty and generality of the proposed framework as well as its limitations. Finally, Section VIII summarizes the presented work. Preliminary results related to this research have been presented in [10] and this paper is a major extension of the previously presented conference paper.. II. RELATED WORK Many image segmentation problems can be formulated as energy optimization problems. The majority of the methods can be divided in two large groups-the optimization in a continuous space and the optimization on a set of discrete variables. In both groups, the key problem lies in two aspects-how can 0278-0062/$31.00 © 2012 IEEE the information (e.g., shape, context) be encoded into the energy function and how can the corresponding energy function be optimized.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Static analysis of multi-staged programs via unstaging translation Static analysis of multi-staged programs is challenging because the basic assumption of conventional static analysis no longer holds: the program text itself is no longer a fixed static entity, but rather a dynamically constructed value. This article presents a semanticpreserving translation of multi-staged call-by-value programs into unstaged programs and a static analysis framework based on this translation. The translation is semantic-preserving in that every small-step reduction of a multi-staged program is simulated by the evaluation of its unstaged version. Thanks to this translation we can analyze multi-staged programs with existing static analysis techniques that have been developed for conventional unstaged programs: we first apply the unstaging translation, then we apply conventional static analysis to the unstaged version, and finally we cast the analysis results back in terms of the original staged program. Our translation handles staging constructs that have been evolved to be useful in practice (typified in Lisp's quasi-quotation): open code as values, unrestricted operations on references and intentional variable-capturing substitutions. This article omits references for which we refer the reader to our companion technical report. Staged programming, which explicitly divides a computation into separate stages, is a unifying principle for the existing programgeneration systems. Partial evaluation [21, 12] , runtime code generation [16, 32, 26, 28] , function inlining, and macro expansion [35, 18] , are all instances of staged computation.. There can be arbitrarily many stages, determined by the nesting depth of program generations: stage 0 is for conventional nonstaged programs, and a program of stage 0 generates a program of stage 1 that generates a program of stage 2, and so on. A program of stage 1 can be brought to stage 0 for execution.. The key aspect of multi-staged languages is to have code templates (program fragments) as first-class values. Code templates are freely passed, stored, composed with code of other stages, and executed when appropriate. For this reason, multi-staged programming is also called "meta-programming.". Multi-staged programming is commonplace in mainstream programming. Lisp(or Scheme)'s quasi-quotation system [35, 18] is a fully fledged multi-staged system that has been evolved to comply with the demands from multi-staged programming practices. C's macros and C++'s templates are multi-staged features. C#, JavaScript, PHP, and Python support a form of multi-staged programming, albeit a limited one. MetaOcaml [36] and Template Haskell [33] are extensions to ML and Haskell respectively to support multi-staged programming.. However, static analysis of multi-staged programs (in order to, for example, find bugs or optimize) is mostly unexplored. Aside from static typing systems such as [25, 4, 13, 31, 3, 37] , there are, as far as we know, no studies on more general and more powerful semantic-based static analysis (á la abstract interpretation) for multi-staged programs.. The primary obstacle is the fact that the basic assumption of conventional static analysis no longer holds: the program text itself is no longer a fixed static entity, but rather a dynamically constructed value. Conventional static analysis can finitely estimate the set of constructed code fragments, but we reach a stalemate after that. If the program executes the generated code, how can we statically analyze the execution ? The program text to analyze at this stage is not a usual text but a finitely abstracted representation of the possibly infinite set of generated code. Static analysis of multi-staged programs is challenging because the basic assumption of conventional static analysis no longer holds: the program text itself is no longer a fixed static entity, but rather a dynamically constructed value.. In this article we have presented a semantic-preserving translation of multi-staged programs into unstaged ones and a static analysis framework based on this translation. Our static analysis approach has three steps: (1) we first apply the unstaging translation; (2) we apply conventional static analysis to the unstaged version; (3) we project the analysis results back in terms of the original staged program. As long as the unstaged static analysis is correct w.r.t. the unstaged semantics, and the projection is safe w.r.t the imaginary staged analysis, a sound static analysis for the original staged programs is obtained. Because directly defining a staged static analysis is difficult, our technique makes it possible to use the knowledge and experience in static analyses of conventional unstaged programs without having to develop staged analyses from scratch.. Our semantics-preserving translation handles staging constructs that have been evolved to be useful in practice (typified in Lisp's quasi-quotation): open code as values, unrestricted operations on references and intentional variable-capturing substitutions. We refer the reader to our companion technical report [6] for the mutable reference cases and complete proofs. A translation that makes the order of evaluation explicit was previously given by Davies and Pfenning [14] . The translation in Figure 8 follows the same principles. Their translation, however, is not an unstaging one. Recently, a program logic for Mini-ML e was presented [2] which precisely captures the operational semantics, yet cannot be realizable as an automatic static analysis. An unstaging translation was previously discussed by Kameyama et al. [23] but has several limitations for our purpose. Their translation is to System F with tuples, needs type and environment classifier [37] annotations, supports only two stages. Finally, they did not prove the translation's semantics preservation property.. Another idea of translation of staged expressions is given by Chen and Xi [4] . They convert boxed expressions to first-order abstract syntax expressions in a second-order language with recursion. An advantage of this representation is that inverse translation becomes straightforward. Chen and Xi use deBruijn indices to represent program variables inside code templates. This has the problem that a binding at a higher stage may disappear or occur unexpectedly [4] . (Such an example is given by Kim et al. [25, §6.4] .). Our translation is in principle similar to Minamide et al. [30] 's closure conversion where free variables inside lambdas become environment loop operations, though their translation is a typedirected one for conventional unstaged programs.. Our translation is an improvement of [1] : we refined the admin reductions to only two kinds and showed that these two admin reductions suffice to reach an admin-normal form that can be converted back to the corresponding staged expression using an inverse translation. The refined proof of semantic preservation and the existence of the inverse translation is new.. From the perspective of Cousot and Cousot's abstract interpretation-based program transformation framework [11] , our unstaging translation can be seen as being derivable by an abstract interpretation of the staged language λS .. Most static analyses for multi-staged programs are string analyses for programs that generate code as strings (a.k.a. heterogeneous meta programs), but they are limited to estimate only the shape, not the semantics, of generated code by using a grammar [7, 29, 5] or the parsing stack [15] . Such string analyses can not analyze the semantics of the generated code string.. Multi-staged static type systems [13, 37, 25, 40] and their inference algorithms are limited forms of staged static analyses. Any extension to estimate other properties than types (á la effect type systems [27, 22, 39] ) is limited to those that can proceed without analyzing the semantics of the generated code. Existing multi-staged static type systems do not have to analyze the generated code because code-generation expression's type comes with the type of the generated code.. Kamin et al. [24] 's data flow analysis of multi-staged programs combines static and dynamic techniques. Our approach is completely static. Smith et al. [34] presented a static analysis of code templates. Their language is two-staged and code templates are not first-class citizens. Variable bindings do not extend beyond the code templates they are defined in. Our approach does not have this limitation.

B I O O O O B I B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A Comment on the Implementation of the Ziggurat Method We show that the short period of the uniform random number generator in the published implementation of Marsaglia and Tsang's Ziggurat method for generating random deviates can lead to poor distributions. Changing the uniform random number generator used in its implementation fixes this issue.

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Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods In this article we propose two new Multiplicative Bias Correction (MBC) techniques for nonparametric multivariate density estimation. We deal with positively supported data but our results can easily be extended to the case of mixtures of bounded and unbounded supports. Both methods improve the optimal rate of convergence of the mean squared error up to O(n −8/(8+d) ), where d is the dimension of the underlying data set. Moreover, they overcome the boundary effect near the origin and their values are always non-negative. We investigate asymptotic properties like bias and variance as well as the performance of our estimators in Monte Carlo Simulations and in a real data example. In recent literature two multiplicative bias correction ("MBC") techniques were proposed for nonparametric estimation of univariate densities with compact (Hirukawa 2010) and with bounded support (Hirukawa and Sakudo, 2014a ). The applied methods were originally investigated in Jones et al. (1995, "JLN") and in Terrell and Scott (1980, "TS") for symmetric kernel functions. Our purpose is now the extension of these results to multivariate density estimation where the marginals possess bounded supports. As mentioned, our approach can easily be extended to the case where one has more involved supports like mixtures of bounded, compact and unbounded supports. As in Hirukawa and Sakudo (2014a) we will focus on the use of asymmetric kernels which were originally proposed in Chen (1999 Chen ( , 2000 for nonparametric estimation of compact as well as positively supported univariate probability densities. As kernel functions Chen suggested the use of Beta ("B"), Gamma ("G") and the so called Modified Gamma ("MG") densities. During the last years many other choices of kernels were proposed like Log Normal ("LN") and Birnbaum Saunders ("BS") (Jin and Kawczak, 2003) , Inverse Gaussian ("IG") ans Reciprocal Inverse. where ρ h (x) = x h 1(x ≥ 2h) + ( Gaussian ("RIG") (Scaillet, 2004) as well as Generalized Birnbaum Saunders ("GBS") (Marchant et. al, 2013) . For the details of the derivation of Generalized Birnbaum Saunders distributions, in particular the so called generator g, see Leiva (2008) . In a very recent paper Hirukawa and Sakudo (2014b) proposed the use of Generalized Gamma ("GG") densities which are acting as a generator of asymmetric kernel functions. Due to the variety of their introduced parameters, we will only focus on a special case, namely the so called Nakagami m-kernel ("NM"). Given a random sample of observations {X i } The use of asymmetric kernel functions has many advantages like adaptive smoothing, optimal rate of convergence in the mean integrated squared error sense for kernels of order two and due to their construction they obviously avoid a boundary effect without producing negative values of the estimate. Although there are many other boundary correction methods available, this approach seems to be a good and easy implementable method for circumventing the boundary problem of nonparametric density estimation near the origin. To our knowledge there is only one paper concerned with multivariate nonparametric density estimation where asymmetric kernels are employed, namely Bouezmarni and Rombouts (2007) . Given a random sample {(X i1 , ..., X id )} n i=1 of independent and identically distributed random vectors with positively supported marginals, they estimate the unknown joint density function f using a product kernel estimator. where h := (h 1 , ..., h d ) denotes the vector of bandwidths and m= G or MG. They showed that the optimal rate of convergence of the mean integrated squared error for this estimator is of order O(n −4/(4+d) ). We will improve this rate with both of our proposed estimators. The remainder of the article is organized as follows. Section 2 introduces the new estimators and determines asymptotic properties like bias and variance for several choices of the kernel function K. Section 3 includes a short discussion of the selection of the required bandwidths as well as a Monte Carlo study. Section 4 concludes and gives an outlook of what could be done in further research investigations. All proofs are postponed to the Appendix. This paper has proposed two new MBC techniques for nonparametric density estimation of multivariate bounded data which reduce the order of magnitude of the bias from O(h) to O(h 2 ). It is demonstrated that both classes of estimators which where originally investigated in Hirukawa (2010) for compact supported and in Hirukawa and Sakudo (2014a) for positively supported data can be extended to the multivariate setting. The variance is not influenced by this procedure and both estimators possess a MSE of order. Moreover the results of the Monte Carlo simulations reveal the superior performance of the JLN estimator especially compared to the classical one. This observation coincides with the univariate results from Hirukawa (2010) as well as Hirukawa and Sakudo (2014a) .. Further research can be done in applying these methods in nonparametric multivariate regression models as it was proposed in Hjort and Glad (1995) in the univariate setting. Moreover it could be interesting to use the proposed Beta kernel estimators for nonparametric estimation of copula densities, see for example Charpentier et al. (2007) . Both topics are under investigation and will be covered in seperate papers.

O O O O O O O O O O O B I O O O O O O O O O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A Case for Continuous Data Protection at Block Level in Disk Array Storages Abstract-This paper presents a study of data storages for continuous data protection (CDP). After analyzing the existing data protection technologies, we propose a new disk array architecture that provides Timely Recovery to Any Point-in-time, referred to as TRAP. TRAP stores not only the data stripe upon a write to the array but also the time-stamped Exclusive ORs (XORs) of successive writes to each data block. By leveraging the XOR operations that are performed upon each block write in today's RAID4/5 controllers, TRAP does not incur noticeable performance overhead. More importantly, TRAP is able to recover data very quickly to any point-intime upon data damage by tracing back the sequence and history of XORs resulting from writes. What is interesting is that the TRAP architecture is very space efficient. We have implemented a prototype of the new TRAP architecture using software at the block level and carried out extensive performance measurements using TPC-C benchmarks running on Oracle and Postgres databases, TPC-W running on a MySQL database, and file system benchmarks running on Linux and Windows systems. Our experiments demonstrated that TRAP not only is able to recover data to any point-in-time very quickly upon a failure but also uses less storage space than traditional daily incremental backup/snapshot. Compared to the state-of-the-art CDP technologies, TRAP saves disk storage space by one to two orders of magnitude with a simple and a fast encoding algorithm. In addition, TRAP can provide two-way data recovery with the availability of only one reference image in contrast to the one-way recovery of snapshot and incremental backup technologies. T HE RAID architecture [1] has been the most prominent architecture advance in disk I/O systems for the past two decades. RAID1 provides 2xN data redundancy to protect data, while RAID3 through RAID5 store data in parity stripes across multiple disks to improve space efficiency and performance over RAID1. The parity of a stripe is the Exclusive OR (XOR) of all data chunks in the stripe. If a disk failed at time t t 0 and the system found such a failure at time t t 1 , the data in the failed disk can be recovered by doing the XOR among the good disks, which may finish at t t 2 . The recovered data is exactly the same image of the data as it was at time t t 0 . There are recent research results that are able to recover data from more than one disk failure [2] , [3] , [4] , [5] , improving the data reliability further.. The question to be asked is: "Can we recover data at time t t 2 to the data image of t t 0 after we found out at time t t 1 that data was damaged by human errors, software defects, virus attacks, power failures, or site failures?". With the rapid advances in networked information services coupled with the maturity of disk technology, data damage and data loss caused by human errors, software defects, virus attacks, power failures, or site failures have become more dominant, accounting for 60 percent [6] to 80 percent [7] of data losses. Recent research [8] , [9] has shown that data loss or data unavailability can cost up to millions of dollars per hour in many businesses. The current RAID architecture cannot protect data from these kinds of failures because damaged data are not confined to one or two disks.. Traditional techniques protecting data from the above failures are mainly periodical (daily or weekly) backups and snapshots [10] , [11] , [12] . These techniques usually take a long time to recover data [13] . In addition, the data between backups are vulnerable to data loss. More importantly, a recent research study has shown that 67 percent of backup data cannot be recovered in the real world [14] . While this fact is well known, there has been no research study on why this is the case. Therefore, it remains unclear and an open question why such high percentage of data recovery failed.. This paper presents an analytical study on snapshot and backup technologies from the block-level storage point of view. Our investigation uncovers the limitations of the existing data protection technologies and provides theoretical explanations as to why so many data recoveries (over 67 percent recoveries) failed using these existing technologies. We show mathematically the data recovery capabilities and limitations of the existing technologies.. Based on our theoretical results, we propose a new storage architecture that overcomes the limitations of existing technologies. We provide a mathematical proof of the correctness of the new data protection technique. Besides being able to recover data damaged by various types of failures, our new architecture provides Timely Recovery to Any Point-in-time, hence named TRAP architecture. The TRAP architecture has optimal space and performance characteristics [15] . The idea of the new TRAP architecture is very simple. Instead of providing full redundancy of data in the time dimension, i.e., keeping a log of all previous versions of changed data blocks in time sequence [13] , [16] , [17] , we compute XORs among changed data blocks along the time dimension to improve performance and space efficiency. With a simple and fast encoding scheme, the new TRAP architecture presents great space savings because of the content locality that exists in real-world applications.. We have implemented a prototype of the new TRAP architecture at the block level using the standard iSCSI protocol. The prototype is a software module inside an iSCSI target mountable by any iSCSI-compatible initiator. We install the TRAP prototype on PC-based storage servers as a block-level device driver and carry out experimental performance evaluation as compared to traditional data recovery techniques. Linux and Windows systems and three types of databases, Oracle, Postgres, and MySQL, are installed on our TRAP prototype implementation. Realworld benchmarks such as TPC-C, TPC-W, and file system benchmarks are used as workloads driving the TRAP implementation under the databases and file systems. Our measurement results show improvements of up to two orders of magnitude of the new TRAP architecture over existing technologies in terms of storage space efficiency. Such order-of-magnitude improvements are practically important given the exponential growth of data [18] . We have also carried out data recovery experiments by selecting any point-in-time in the past and recovering data to that time point. Experiments have shown that all recovery attempts are successful. The recovery time of the new TRAP architecture is compared with that of existing reliable storage architectures to show that the new TRAP architecture can recover data to any point-in-time very quickly.. We analyze the capabilities and limitations of existing data protection technologies in the next section. The detailed design and implementation of the new TRAP architecture is presented in Section 3. Section 4 discusses the system design and implementation, and Section 5 presents the experimental settings and the workload characteristics. Numerical results and discussions are presented in Section 6. Related work is discussed in Section 7. We conclude our paper in Section 8. We have presented a novel disk array architecture capable of providing Timely Recovery to Any Point-in-time for CDP, referred to as the TRAP architecture. A prototype of the new TRAP architecture has been implemented as a block-level device driver. File systems such as ext2 and NTFS and databases such as Oracle, Postgres, and MySQL have been installed on the prototype implementation. Realworld benchmarks including TPC-C, TPC-W, and file system benchmarks are used to test the performance of the new storage architecture. Extensive experiments have demonstrated improvements of up to two orders of magnitude in terms of storage efficiency. In addition, we have given theoretical proofs for the one-way recovery of traditional snapshots and incremental backups compared to the two-way recovery of the TRAP architecture. Recovery experiments have also been carried out several dozen times to show the quick recovery time of the new architecture. Measurements have also shown that the new architecture has little negative performance impact on application performance while providing CDP capability. Depending on the different values of RPO and RTO, there exist different storage architectures capable of recovering data upon an outage. We summarize existing related works in three different categories based on different RPOs.. Snapshot or incremental backup. Data protection and recovery have traditionally been done using periodical backups [10] , [12] and snapshots [11] . Typically, backups are done nightly when data storage is not being used since the process is time consuming and degrades application performance. During the backup process, user data are transferred to a tape, a virtual tape, or a disk for disk-to-disk backup [10] , [34] . To save backup storage, most organizations perform full backups weekly or monthly with daily incremental backups in between. Data compression is often used to reduce the backup storage space [12] , [35] . A good survey of various backup techniques can be found in [12] . Snapshot is a functionality that resides in most modern disk arrays [36] , [37] , [38] , file systems [34] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , volume managers [46] , [47] , NAS filers (network attached storages) [48] , [49] , [50] , and backup software. A snapshot is a point-in-time image of a collection of data allowing online backup. A full-copy snapshot creates a copy of the entire data as a read-only snapshot storage clone. To save space, the COW snapshot copies a data block from the primary storage to the snapshot storage upon the first write to the block after the snapshot was created [47] . A snapshot can also redirect all writes to the snapshot storage [11] , [49] after the snapshot was created. Typically, snapshots can be created up to a half dozen a day [46] without significantly impacting application performance.. File versioning. Besides periodical data backups, data can also be protected at the file system level using file versioning, which records a history of changes to files. Versioning was implemented by some early file systems such as the Cedar File System [41] , 3DFS [51] , and CVS [52] to list a few. Typically, users need to create versions manually in these systems. There are also COW versioning systems exemplified by Tops-20 [53] and VMS [54] that have automatic versions for some file operations. Elephant [45] transparently creates a new version of a file on the first write to an open file. CVFS [55] versions each individual write or small metadata using highly efficient data structures. OceanStore [56] uses versioning not only for data recovery but also for simplifying many issues with caching and replications. The LBFS [57] file system exploits similarities between files and versions of the same files to save network bandwidth for a file system on low-bandwidth networks. Peterson and Burns have recently implemented the ext3cow file system that brings snapshot and file versioning to the open source community [40] . Other programs such as rsync, rdiff, and diff also provide versioning of files. To improve efficiency, flexibility, and portability of file versioning, Muniswamy-Reddy et al. [58] presented a lightweight user-oriented versioning file system called Versionfs that supports various storage policies configured by users.. File versioning provides a time-shifting file system that allows a system to recover to a previous version of files. These versioning file systems have controllable RTO and RPO. But they are generally file system dependent and may not be directly applicable to enterprise data centers that use different file systems and databases.. Traditional CDP. To provide timely recovery to any point-in-time at the block level, one can keep a log of changed data for each data block in a time sequence [13] , [16] , [59] . In the storage industry, this type of storage is usually referred to as the CDP storage. Laden et al. proposed four alternative architectures for CDP in a storage controller and compared them analytically with respect to both write performance and space usage overhead [60] . Zhu and Chiueh proposed a userlevel CDP architecture that is both efficient and portable [61] . They implemented four variants of this CDP architecture for NFS servers and compared their performance characteristics. Lu et al. presented an iSCSI storage system named Mariner to provide comprehensive CDP on commodity ATA disk and Gigabit Ethernet technologies [62] . The main drawback of the CDP storage is the huge amount of storage space required, which has thus far prevented it from being widely adopted. There have been research efforts attempting to reduce the storage space requirement for traditional CDP. Flouris and Bilas [63] proposed a storage architecture named Clotho providing transparent data versioning at the block level. Clotho coalesces the updates that take place within a period of time by creating new versions for them. This versioning happens at discrete time points, not necessarily continuous as done in CDP. What is interesting in their work is that they observed storage space savings by binary differential compression to store only the delta data that has been modified since the last version. Morrey III and Grunwald [16] observed that for some workloads, a large fraction of disk sectors to be written contain identical content to previously written sectors within or across volumes. By maintaining information (128-bit content summary hash) about the contents of individual sectors, duplicate writes are avoided. Zhu et al. [35] proposed an efficient storage architecture that identifies previously stored data segments to conserve storage space. A recent study [64] described three techniques to avoid the disk bottleneck in the Data Domain deduplication file system. These data reduction techniques generally require a search in the storage for an identical data block before a write is performed. Such a search operation is generally time consuming, although a smart search algorithm and intelligent cache designs can help in speeding up the process [16] , [35] . These data reduction techniques are more appropriate for periodic backups or replications where timing is not as much a critical concern as the timing of online storage operations.. It should be noted that keeping a log of changed data has been studied and used in other contexts other than data recovery. For example, the log-structured file system has been researched extensively for improving disk write performance [65] , [66] . There are variations of such logstructured file system, such as DCD [28] proposed by Hu and Yang and Vagabond [67] proposed by Norvag and Bratbergsengen for optimizing disk write performance. Norvag and Bratbergsengen also noticed the space savings of storing a delta object in the buffer space when an object is changed, which suggests that data locality exists in write operations. Using our implementation described in the last section, we install our TRAP on a PC serving as a storage server, shown in Fig. 4 . There are four PCs that are interconnected using Intel's NetStructure 10/100/1,000 Mbps 470T switch. Two of the PCs act as clients running benchmarks. One PC acts as an application server. The hardware characteristics of the four PCs are shown in Table 1 .. In order to test our TRAP under different applications and different software environments, we set up both Linux and Windows operating systems (OSs) in our experiments. The software environments on these PCs are listed in Table 1 . We install Fedora 4 (Linux Kernel 2.6.9) on one of the PCs and Microsoft Windows XP Professional on the other PCs. On the Linux machine, the UNH iSCSI implementation [26] is installed. On the Windows machines, the Microsoft iSCSI initiator [27] is installed. Since there is no iSCSI target on Windows available to us, we have developed our own iSCSI target for Windows. After installing all the OS and iSCSI software, we install our TRAP module on the storage server PC inside the iSCSI targets.. On top of the TRAP module and the OSs, we set up three different types of databases and two types of file systems. Oracle Database 10g is installed on Windows XP Professional. Postgres Database 7.1.3 is installed on Fedora 4. MySQL 5.0 database is set up on Windows. Ext2 and NFTS are the file systems used in our experiments. To be able to run real-world Web applications, we install a Tomcat 4.1 application server for processing Web application requests issued by benchmarks.

O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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