Axel Hutt

Nicolas Rougier

Numerical simulation scheme of one-and two dimensional neural fields involving space-dependent delays

Introduction

Finite transmission speed in physical systems has attracted research for decades. Previous work on heat diffusion has shown experimentally that the transmission speed (also called propagation speed in the literature) is finite in certain media [START_REF] Lazzaro | Fast heat pulse propagation in hot plasmas[END_REF][START_REF] Klossika | Importance of a finite speed of heat propagation in metals irradiated by femtosecond laser pulses[END_REF]. These results do not show accordance to classical diffusion theory implying infinite transmission speed. To cope with this problem theoretically, Cattaneo was one of the first to insert delay terms into the diffusion equation to achieve a finite transmission speed [START_REF] Cattaneo | A form of heat conduction equation which eliminates the paradox of instantaneous propagation[END_REF].

Recently, an integral model has been proposed which takes into account a finite transmission speed as a space-dependent retardation [START_REF] Hutt | Generalization of the reaction-diffusion, Swift-Hohenberg, and Kuramoto-Sivashinsky equations and effects of finite propagation speeds[END_REF]. It was shown that the Cattaneo-equation can be derived from this model. This model is well-established in computational neuroscience and known as the neural field model. It describes the activity evolution in a neural population involving finite transmission speed along axonal fibres. The neural field model has been shown to model successfully neural activity known from experiments [START_REF] Huang | Spiral waves in disinhibited mammalian neocortex[END_REF][START_REF] Bressloff | What geometric visual hallucinations tell us about the visual cortex[END_REF]. In the recent decades, neural fields have been studied analytically and numerically in one and two spatial dimensions [START_REF] Venkov | Dynamic instabilities in scalar neural field equations with space-dependent delays[END_REF][START_REF] Laing | Spiral waves in nonlocal equations[END_REF], while previous studies considered finite axonal transmission speeds in one-dimensional models only [START_REF] Coombes | Waves, bumps and patterns in neural field theories[END_REF][START_REF] Hutt | Pattern formation in intracortical neuronal fields[END_REF][START_REF] Atay | Stability and bifurcations in neural fields with finite propagation speed and general connectivity[END_REF][START_REF] Atay | Neural fields with distributed transmission speeds and constant feedback delays[END_REF]. To our best knowledge, only few previous studies considered analytically and numerically finite transmission speeds in two-dimensional neural fields. The current work presents a recently developed method [START_REF] Hutt | Activity spread and breathers induced by nite transmission speeds in two-dimensional neural fields[END_REF] to reveal finite transmission speed effects in two-dimensional systems. The subsequent paragraphs derive a novel fast numerical scheme to simulate the corresponding evolution equations in one and then in some detail in two spatial dimensions. Stimulus-induced activity propagation in two spatial dimensions is studied numerically to illustrate the delayed activity spread. We find numerically transmission delay-induced breathers.

The underlying model considers a one-dimensional line Ω with length l or a two-dimensional rectangle spatial domain Ω with side length l, in both cases assuming periodic boundary conditions. In addition, the center of the coordinate system is chosen to be the center of the domain in the following. Then the neural population activity V (x,t), i.e. the mean membrane potential, at spatial location x 2 Ω and time t obeys the evolution equation

τ ∂ ∂t V (x,t)=I(x,t) -V (x,t)+ Z Ω d n yK(|x -y|)S  V ✓ y,t - |x -y| c ◆ (1)
with n = 1 or n = 2, the synaptic time constant τ, the external stimulus I(x,t), the finite axonal transmission speed c and the nonlinear transfer function S. Moreover, the spatial interaction is non-local and is given by the spatial synaptic connectivity kernel K(|x-y|), that depends on the distance between two spatial locations x and y only.

The novel principle

For notational simplicity, let us consider a one-dimensional spatial domain. Then the integral on the right hand side of Eq. ( 1) can be re-written as

Z Ω dz K(|x -z|)S  V ✓ z,t - |x -z| c ◆ = Z Ω dz Z ∞ -∞ dt 0 δ ✓ |x -z| c -(t -t 0 ) ◆ K(|x -z|)S[V (z,t 0 )] = Z Ω dz Z ∞ -∞ dt 0 L(x -z,t -t 0 )S[V (z,t 0 )] = Z Ω dz Z τ max 0 dτL(x -z, τ)S[V (z,t -τ)],
with τ max = l/c. This shows that the introduction of the space-time kernel L(x,t)= K(x)δ (|x|/ct) allows us to write the single space integral as two integrals: one spatial convolution and one integral over delays. To understand the logic of the computation, let us discretize the time and space by t ! t n = n∆t, x ! x m = m∆x with n 2 N 0 , m 2 Z 0 , |m| < M/2 and l = M∆x. This implies that the speed c also takes discrete values. We obtain

L(x,t) ! L(x m ,t n ) ⇠ K(m∆x)δ ((∆x/c)|m|-n∆t) = K m δ ✓ ∆t ✓ ∆x c∆t |m|-n ◆◆ = K m δ (∆t (r|m|-n)) = K m δ (|m|∆t (r -n/|m|)) ⇠ K m δ |m|,n/r
with K m = K(m∆x), r = ∆x/(c∆t). The last equation shows that L(x m ,t n ) ⇠ K ±n/r 6 = 0 only if r is rational number with r = n/m and thus

c = ∆x ∆t 1 r = ∆x ∆t m n is discrete.

The numerical implementation in two spatial dimensions

To investigate the activity propagation in detail, we derive a novel iteration scheme for the numerical integration of (1) for n = 2. Since the integral over space in [START_REF] Atay | Stability and bifurcations in neural fields with finite propagation speed and general connectivity[END_REF] is not a convolution in the presence of a finite transmission speed c, one can not apply directly fast numerical algorithms such as the Discrete Fast Fourier Transform (DFT) to calculate the integral. Hence the numerical integration of ( 1) is very time consuming with standard quadrature techniques. For instance, with a discretization of the spatial domain by N 2 grid intervals and applying the Gaussian quadrature rule for the spatial integral, it would be necessary to compute N 4 elements in each time step which is very time-consuming in the case of a good spatial resolution. The work [START_REF] Hutt | Activity spread and breathers induced by nite transmission speeds in two-dimensional neural fields[END_REF] proposes a fast numerical method that is based on the DFT and resembles the Ritz-Galerkin method well-established to solve partial differential equations. As in the previous section, the integral in (1) reads

A(x,t)= Z Ω d 2 yK(|x -y|)S  V ✓ y,t - |x -y| c ◆ = Z Ω d 2 y Z ∞ -∞ dt 0 δ ✓ |x -y| c -(t -t 0 ) ◆ K(|x -y|)S[V (y,t 0 )] = Z Ω d 2 y Z ∞ -∞ dt 0 L(x -y,t -t 0 )S[V (y,t 0 )] (2)
= Z Ω d 2 y Z τ max 0 dτL(x -y, τ)S[V (y,t -τ)], (3)
with τ max = l/ p 2c, the novel spatial delay kernel L(x, τ)=K(x)δ (|x|/c -τ) and the delta-distribution δ (•). These simple calculations show that A may be written as a two-dimensional spatial convolution, but with a new delayed spatio-temporal kernel L that now considers the past activity. The form (2) has been used previously to study spatio-temporal instabilities in one-and two-dimensional neural fields [START_REF] Venkov | Dynamic instabilities in scalar neural field equations with space-dependent delays[END_REF].

The new delay kernel L is independent of time t and is computed on the delay interval only. Hence it represents the contribution of the current and past activity to the current activity at time t. In addition A implies multiple delays and the corresponding delay distribution function depends strongly on the spatial kernel K. In other words, axonal transmission speeds represent a delay distribution as found before in other contexts [START_REF] Hutt | Critical fluctuations and 1/f -activity of neural fields involving transmission delays[END_REF][START_REF] Faye | Some theoretical and numerical results for delayed neural field equations[END_REF].

K v ∆ t t i m e L 4 L 3 L 2 L 1 L 0 v ∆ t Figure 1:
The construction of the delay-kernel L(x, τ). Assuming a spatial kernel (left image), L exhibits rings with radius cτ (images on the right for different delay times) which is the interaction distance of the system at the delay time τ.

Figure 1 illustrates the construction of the kernel: given the kernel function K in space (Fig. 1, left), L(x, τ) is generated by cutting out a ring of radius cτ (Fig. 1, right hand side). In a continuous spatial domain these rings are infinitely thin, whereas a spatially discretized domain yields finite ring widths, see the paragraphs below for more details. Now let us derive the rules to compute A numerically. The periodic boundary conditions implied lead to discrete wave vectors

k mn =(k m , k n ) with k p = 2π p/l, p 2 Z 0 . The Fourier series of V (x,t) reads V (x, y,t)= 1 l ∞ ∑ m,n=-∞ Ṽmn (t)e i(k m x+k n y) (4)
with the Fourier vector component Ṽmn (t)= Ṽ (k m , k n ,t) and the spatial Fourier transform

Ṽmn (t)= 1 l Z l/2 -l/2 dx Z l/2 -l/2 dyV(x, y,t)e -i(k m x+k n y) . (5)
Inserting ( 4) into (3) and applying (5) leads to

A(x, y,t)= ∞ ∑ m,n=-∞ e i(k m x+k n y) Z τ max 0 dT Lmn (T ) Smn (t -T ), (6)
with the spatial Fourier transforms of L(x,t) Lmn (t), Smn (t) and the nonlinear functional

S[V (x,t)]. Moreover Lmn (T )= c 2 l Z l/2c -l/2c Z l/2c -l/2c δ (|τ|-T )K(|cτ|)e -ick mn τ d 2 τ . (7)
After obtaining A(x, y,t) in the Fourier space for a continuous spatial domain, now we discretize the spatial domain to gain the final numerical scheme. To this end, Ω is discretized in a regular spatial grid of N ⇥ N elements with grid interval ∆x = l/N. Hence x ! x n = n∆x, n = -N/2,...,N/2 -1. By virtue of this discretization, we can approximate ( 6) and ( 7) by applying the rectangular rule

R b a f (x)dx ⇡ ∆x ∑ N/2-1 n=-N/2 f (x n ). The error is E < (b -a)∆x 2 f 00 (ξ )/24, a < ξ < b
for twice-differentiable functions f , i.e. the rectangular rule is a good approximation for smooth functions and large enough N. The same holds true for the discretization of the time integral and Eq. [START_REF] Faye | Some theoretical and numerical results for delayed neural field equations[END_REF] reads

Lmn (T u )= l N 2 ∆t N/2 ∑ k,p=-N/2 L kp (T u ) e -i2π(km+np)/N (8)
with the discrete version of the delay kernel L L kp (T u )=δ (∆τ

p k 2 + p 2 , T u )K(|x kp |).
The symbol δ (•, •) is identical to the Kronecker symbol and is introduced for notational convenience. By virtue of the isotropy of the spatial interactions, in addition we find the simple relation

L kp (T u )=K(uc∆t).
In other words the width of the rings in Fig. 1 is c∆t. In these latter calculations, we introduced the time discretization

τ kp =(k, p)∆τ, ∆τ = ∆x/c, T ! T u = u∆t and δ (τ -T ) ! δ nu /∆t for τ ! τ n .
Although the relation L kp (T u )=K(uc∆t) seems to be quite intuitive and elucidates the discrete ring structure of L, it does not give directly the condition which grid point (k, p) belongs to which delay ring. This condition may be read off the Kronecker symbol: u is an integer number and hence δ (∆τ Moreover, the definition of L kp (T u ) allows us to derive some conditions on the numerical parameters. The ring width in Fig. 1 is ∆r = c∆t/∆x which is the number of spatial grid intervals. Hence the maximum radius of a ring is l/ p 2∆x and hence the maximum transmission speed that can be implemented is c max = l/ p 2∆t. Since c max ! ∞ for ∆t ! 0, the transmission speed c > c max in the discrete scheme is equivalent to an infinite transmission speed in the analytical original model and the finiteness of c max results from the time discretization. Moreover, c ! c max yields τ max ! 0, i.e. the transmission delay vanishes. We add that the maximum wave number is k max = 2π/∆x and, by the definition of ∆x, the number of Fourier modes is limited to N.

p k 2 + p 2 , T u )=1 if [∆τ p k 2 + p 2 /
Combining the latter results now Eq. (6) reads

A(x r , y s ,t v )= N/2-1 ∑ m,n=-N/2 e i2π(mr+ns)/N ⇥ u max -1 ∑ u=0 Lmn (T u ) Smn (t v -T u ) . ( 9
)
With the standard definition of the two-dimensional Discrete Fourier Transform

DFT [A] kp = ∑ n,m
A nm e -i2π(nk+mp)/N , n, m 2 [-N/2; N/2 -1] and its inverse (IDFT) correspondingly, we find finally

A(x,t v )= l 2 N 2 IDFT " u max -1 ∑ u=0 DFT [L(T u )] ⇥ DFT [S(t v -T u )] # . ( 10
)
Some numerical implementations of the DFT assume that the index n runs in the interval [0; N -1]. In this case, Eq. ( 10) is also valid but DFT [A] kp is modulated by a factor e -iπ(k+p) =(-1) k+p .

In practice, DFT [L(T u )] is computed once for all T u in the beginning of the simulation since it does not depend on the system activity. Moreover, for N = 2 n , n 2 N , the discrete Fourier Transform may be implemented numerically by a Fast Fourier transform, that speeds up the numerical computation dramatically. This possible algorithm choice represents the major advantage of the proposed method compared to other non-convolution methods.

The discrete version of A can be applied to any explicit or implicit numerical integration scheme. For instance, the numerical Euler scheme stipulates

Ṽmn (t i + ∆t)= Ṽmn (t i )+ ∆t τ (I mn (t i ) -Ṽmn (t i ) + ∆t τ L 3 N 4 d ∑ u=0 DFT [L(t u )] mn ⇥ DFT [S(t v -t u )] mn ) ( 11
)
where I mn (t) is the Fourier transform of the input I(x,t) and one obtains V (x,t v ) by applying Eq. ( 4).

In the following, we study analytically and numerically the response to an external stimulus. At first, let us consider a small input. Then the response is linear about the systems' stationary state. Since we are interested in responses that approach the stationary state after removal of the stimulus, it is necessary to ensure the linear stability of the stationary state. The stationary state of Eq. (1) constant in space and time implies V 0 = κS[V 0 ]+I 0 for a constant input I 0 with the kernel norm κ = R Ω K(x)d 2 x. Considering small additional external inputs Ī(x,t)=I(x,t) -I 0 , small deviations u(x,t)=V (x,t) -V 0 from this stationary state obey

du(x,t) dt = -u(x,t)+ Ī(x,t)+s 0 Z Ω K(x -y)u (y,t -|x -y|/c) dy 2 . ( 12
)
with s 0 = δ S[V ]/δV,V = V 0 . Now expanding u(x,t) into a spatial Fourier series according to Eq. ( 4) and applying a temporal Laplace transform to each Fourier mode amplitude, we find the characteristic equation

λ + 1 = Z Ω K(x)e ikx-λ |x|/c d 2 x ( 13
)
with the wave vector k =(k m , k n ) t and the Lyapunov exponent λ 2 C . The stationary state V 0 is linearly stable if Re(λ ) < 0. Now let us consider the spatio-temporal response of the system involving the spatially periodic interactions

K(x)=K o 2 ∑ i=0 cos(k i x) exp(-|x|/σ )
with

k i = k c (cos(φ i ), sin(φ i )) t , φ i = iπ/3 .
This kernel reflects spatial hexagonal connections which have been found, e.g., in layer 2/3 of the visual cortex in monkeys [START_REF] Lund | Anatomical substrates for functional columns in macaque monkey primary visual cortex[END_REF]. Stimulating the stable system by a small external input in the presence of the finite transmission speed c elucidates the transmission delay effect on the linear response. This delay effect has attracted some attention in previous studies on the activity propagation in the visual cortex [START_REF] Schwabe | The role of feedback in shaping the extra-classical receptive field of cortical neurons: a recurrent network model[END_REF][START_REF] Bringuier | Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons[END_REF]. For the given kernel, the characteristic equation ( 13) reads

λ + 1 = 2 ∑ i=0 f + (λ , φ i )+ f -(λ , φ i ) with f ± (λ , φ i )=1/ q (1/σ + λ /c) 2 + k 2 + k 2 c ± 2kk c cos(φ i -θ ) 3
and k = k(cos(θ ), sin(θ )) t . The numerical simulation applies parameters which guarantee the stability of the stationary state.

Figure 2 shows snapshots of the simulated spatio-temporal response of the system about a stable stationary state applying the numerical scheme [START_REF] Hutt | Pattern formation in intracortical neuronal fields[END_REF]. We observe the lateral activity propagation starting from the stimulus location in the domain centre. The spreading activity reveals the maxima of axonal connections close to previous experimental findings [START_REF] Lund | Anatomical substrates for functional columns in macaque monkey primary visual cortex[END_REF]. To validate the numerical results, we take a closer look at two single spatial locations, denoted A and B in Fig. 2 at distance d A and d B from the stimulus location in the center. Before stimulus onset, they show the stationary activity constant in time. After stimulus onset, it takes the activity some time to propagate from the stimulus location to these distant points, e.g. the transmission delays d A /c = 3.3ms and d B /c = 6.2ms. Figure 2 shows that the activity reaches the locations A and B about these times for the first time as expected. This finding validates the numerical algorithm proposed above. We investigate whether the transmission delay induces oscillatory instabilities in the presence of external input. The following brief numerical study is motivated by previous theoretical studies on breathers [START_REF] Folias | Breathers in two-dimensional excitable neural media[END_REF]. In that study, the authors computed analytically conditions for Hopf-bifurcations from stimulus-induced stable standing bumps in a neural model involving spike rate adaption. The presence of the spike rate adaption permits the occurence of the Hopf-bifurcation. The corresponding control parameter of these instability studies is the magnitude of the applied external stimulus. In contrast, the present model does not consider spike rate adaption to gain a Hopf-bifurcation, but consider tranmsission delays. We decreases the axonal transmission speed from large speeds, i.e. increases the transmission delay, to evoke a delay-induced Hopf-bifurcation while keeping the other parameters constant. Let us assume an anisotropic Gaussian stimulus

I(x,t)=I 0 e -x t Σ -1 x/2
with the 2 ⇥ 2 diagonal variance matrix Σ -1 with Σ -1 ii = 1/σ 2 i , i = 1, 2. Moreover the spatial kernel K(x) represents locally excitatory and laterally inhibitory connections and the transfer function is the Heaviside function S

[V ]=H[V -V thresh ].
The numerical computation of Eq. (1) applying the numerical scheme (11) yields delay-induced breathers in two dimensions. Figure 3 shows the temporal sequence of a single oscillation cycle. To our best knowledge such delay-induced breathers in two dimensions have not been found before.

Conclusion

We have motivated briefly a one-dimensional numerical method to integrate a spatial integral involving finite transmission speeds Moreover we have derived analytically and validated numerically in detail a novel numerical scheme for twodimensional neural fields involving transmission delay that includes a convolution structure and hence allows the implementation of fast numerical algorithms, such as Fast Fourier Transform. We have demonstrated numerically a transmission delay-induced breather [START_REF] Hutt | Activity spread and breathers induced by nite transmission speeds in two-dimensional neural fields[END_REF]. To facilitate future applications of the algorithm, the implementation code for both numerical examples is made available for download 1 . We point out that the method can be easily extended to higher dimensions.

In future research, the transmission delay will play an important role in the understanding of fast activity propagations whose time scales are close to the transmission delay, e.g. in the presence of ultra-fast pulses and/or at spatial nanometer scales. An open source Graphical User Interface written in Python for a user-

Figure 2 :

 2 Figure 2: Spatio-temporal response activity to the external stimulus I(x,t)= I 0 + e -x 2 /σ 2 I for the spatial connectivity function K(x) given by the numerical simulation of Eq. (1). Used (dimensionless) parameters are K o = 0.1, c = 10, l = 10, k c = 10π/l, σ = 10, σ I = 0.2, N = 512, τ = 1, ∆t = 0.005. Moreover, I 0 = 2.0, S[V ]=2/(1 + exp(-5.5(V -3))) and V 0 = 2.00083. The initial values are chosen to V (x, θ )=V 0 for the delay interval -l/ p 2c  θ  0. Introducing the temporal and spatial scale scale τ = 10ms and λ = 1.0mm, the results reflect the spatio-temporal activity with transmission speed c = 1.0m/s and the domain length l = 10mm, which are realistic values for layer 2/3 in visual cortex. Then the points A and B are located at a distance d A = 2.1mm and d B = 3.8mm from the stimulus onset location at the origin, respectively. The bar in the plots is 0.83mm long.

Figure 3 :

 3 Figure 3: One cycle of a transmission delay-induced breathers evoked by an anisotropic external stimulus. The spatial connectivity function is chosen to K(r)=10 exp(-r/3)/(18π) -14 exp(-r/7)/(98π) and the input magnitude and variances are I 0 = 10 and Σ -1 11 = 3, Σ -1 22 = 5, respectively. Other parameters are c = 100, l = 30, N = 512, τ = 1, ∆t = 0.05 and V thresh = 0.005. The initial values are chosen to V (x, θ )=0 for the delay interval -L/ p 2c  θ  0.

  ∆t]=u with the integer operation [a] that cuts off the decimal numbers. Consequently the grid points (k, p) that contribute to the delay time T u obey

	u 	∆x c∆t	p k 2 + p 2 < u + 1, u = 0, 1, 2,...,u max
	with u max =[τ max /∆t], i.e. they lie in a ring with inner and outer radius (c∆t/∆x)u
	and (c∆t/∆x)(u + 1), respectively.

http://www.loria.fr/ ˜rougier/research/DNF.html

NeuralFieldSimulator: https://gforge.inria.fr/projects/nfsimulator/

friendly application of the method proposed will be available soon 2 .


Andreas S Rath
email: arath@know-center.atddevaurs@know-center.atslind@know-center.at

Didier Devaurs

Stefanie N Lindstaedt

Detecting Real User Tasks by Training on Laboratory Contextual Attention Metadata

Detecting the current task of a user is essential for providing her with contextualized and personalized support, and using Contextual Attention Metadata (CAM) can help doing so. Some recent approaches propose to perform automatic user task detection by means of task classifiers using such metadata. In this paper, we show that good results can be achieved by training such classifiers offline on CAM gathered in laboratory settings. We also isolate a combination of metadata features that present a significantly better discriminative power than classical ones.

Introduction

Today knowledge workers have to handle incessantly increasing amounts of information, in terms of text documents, emails, etc., located both on their own computer desktops and on the Web. Personal information management and search systems can help coping with this ever growing challenge, and they can do it even more efficiently if they provide contextualized and personalized support. For that they have to take account of the user's usage and contextual attention metadata [SLDH06, WNVD07, VS07, RWK + 08, CDH + 08]1 . Such metadata is especially valuable for detecting the user's task, and several approaches have been proposed for doing so [OSTS06, SLDH06, LFBG07, GKS + 08, RDL09]. By focusing on the user's interactions with applications and resources (user interaction context) we explore how to fully exploit this metadata to make user task detection more efficient in a real work environment.

Related Work: Here, by task detection we mean task class detection also referred to as task classification, as opposed to task switch detection. Task classification deals with the challenge of classifying usage data from user task execution into task classes or task types. Task switch detection involves predicting when the user switches from one task to another [START_REF] Oliver | SWISH: semantic analysis of window titles and switching history[END_REF][START_REF] Shen | A hybrid learning system for recognizing user tasks from desktop activities and email messages[END_REF]. Automatic task detection is classically modeled as a machine learning problem, and more precisely a classification problem. This method is used to recognize Web based tasks [START_REF] Gutschmidt | Paving the path to automatic user task identification[END_REF], tasks within emails [START_REF] Dredze | Automatically classifying emails into activities[END_REF][START_REF] Shen | A hybrid learning system for recognizing user tasks from desktop activities and email messages[END_REF] or from the complete user's desktop [OSTS06, SLDH06, LFBG07, GKS + 08, RDL09]. All these approaches are based on the following steps: (i) The CAM is captured by system and application sensors. (ii) Features, i.e. parts of this data, are chosen to build classification training instances. (iii) To obtain valid inputs for machine learning algorithms, these features are first transformed into attributes [START_REF] Witten | Data Mining: Practical Machine Learning Tools and Techniques[END_REF]. This transformation may include data preprocessing operations, such as removing stopwords [LFBG07, GKS + 08] and application specific terms [START_REF] Oliver | SWISH: semantic analysis of window titles and switching history[END_REF], or constructing word vectors. (iv) Attribute selection [SLDH06, GKS + 08] is performed (optional step) to select the best discriminative attributes for (v) training the classification/learning algorithms.

Contribution: In this paper, while adopting this classical approach for task detection, we focus on investigating the following research questions: (i) How good can the performance of a task classifier be when used in a real work environment, while being trained with CAM gathered in laboratory settings? (ii) Which are the automatically observable CAM features that allow for good task detection performance? Both questions are concerned with work efficiency. The goal of the first one is to determine whether a task classifier can be trained offline, thus saving the user from the burden of manual training during work processes, which might slow down her computer and hence have a negative influence on her work efficiency and user experience. The second one aims at finding the most discriminative features among the automatically captured CAM features of our CAM framework for achieving a good balance between task detection accuracy and classification workload, which influences which CAM sensors have to be developed to do automatic task detection. To get a first impression on the answers to these research questions, we have designed a large-scale experiment in which users have performed a set of tasks both on a single laboratory computer and on their personal workstations. Our first results, achieved with a dataset containing four task classes and 203 task instances from 14 users, indicate that: (i) reliable detection of real tasks via offline training is possible, (ii) the good discriminative power of the classical window title feature [OSTS06, SLDH06, LFBG07, GKS + 08] is confirmed, and (iii) classification accuracy is significantly increased by using a combination of six features specific to our approach.

Outline: In Section 2 we describe our experiment and our CAM framework. Our methodology for task classification is presented in Section 3, and the results obtained from the task classifier are discussed in Section 4. Finally we draw some conclusions in Section 5.

Experiment Design and Execution

Our experiment was carried out in the knowledge-intensive domain of the Know-Center. It was preceded by an analysis phase, during which several requirements were defined, by interviewing knowledge workers. Users required to know what kind of data was recorded, to be able to access and modify it, and that the evaluation results were anonymized. They could practice with the recording tool for a week before the experiment in order to reduce the bias of unfamiliarity during the experiment. This study/experiment was exploratory, the comparison was within subjects and the manipulations were achieved by the environment (laboratory vs. personal workstation) and the executed task (four different tasks).

Manipulation 1 -Work Environment: The first manipulation was achieved by varying the work environment (i.e. the computer desktop environment) of the participants. Each participant performed the same set of tasks both on a laboratory computer on which a set of standard software used in the company had been installed beforehand, and on their company personal workstations with their personal computer desktop settings and access to their personal files, folders, bookmarks, emails and so on. Half of the participants worked first on the laboratory computer and then on their personal workstations, and vice versa for the other half. The assignment of the participants to each group was randomized.

Manipulation 2 -Task: The second manipulation resulted from varying the tasks themselves. During a preliminary meeting, the participants of the experiment agreed on a selection of four tasks typical of the Know-Center domain: (1) "Filling in the official journey form", (2) "Filling in the cost recompense form for the official journey", (3) "Creating and handing in an application for leave" and (4) "Planning an official journey".2 A short questionnaire was issued before starting the experiment to make sure that the probands understood the tasks they had to perform, and also to have them thinking about the tasks before they actually executed them.

During the experiment, for capturing the users' CAM, we have used multiple sensors [RWK + 08] that record the user interactions with resources and applications on the computer desktop (see Table 1). The captured usage data is used to automatically populate our User Interaction Context Ontology (UICO) [START_REF] Rath | UICO: an ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF] which constitutes an ontologybased user context model of the personal information management domain. Rule-based and information extraction techniques are used to automatically enrich our ontology, by discovering new instances of concepts, and deriving inter-concepts relationships [START_REF] Rath | UICO: an ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF]. For a full presentation of the UICO, the interested reader is refered to [START_REF] Rath | UICO: an ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF].

Task Classification Methodology

Our dataset contains 203 task instances from 14 users: 106 tasks from the laboratory computer and 97 from work station computers. The number of representatives for each task class were almost equally distributed (see Table 2). In our experiment we evaluated the influence of five parameters on the task detection performance: (i) the number of features, (ii) the classification model, (iii) the feature category, (iv) single features and (v) the combination of the k top performing single features with k ∈ {2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20}. For the task detection part we used the machine learning toolkit Weka [START_REF] Witten | Data Mining: Practical Machine Learning Tools and Techniques[END_REF] during a task execution. For details about the data preprocessing and the feature to attribute transformation we refer to [START_REF] Rath | UICO: an ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF].

We have defined 50 features that can be grouped in six categories: (i) ontology structure, (ii) content, (iii) application (iv) resource, (v) action and (vi) switching sequences.

The ontology structure category contains features representing the number of instances of concepts and the number of datatype and objecttype relations used per task. The content category consists of the content of task-related resources, the content in focus and the text input of the user. The application category contains the classical window title feature [OSTS06, SLDH06, LFBG07, GKS + 08], the application name feature [GKS + 08] and our newly introduced graphical user interface elements (accessibility objects3 ) features.

The resource category includes the complete contents and URIs (URLs) [START_REF] Shen | A hybrid learning system for recognizing user tasks from desktop activities and email messages[END_REF] of the used, referenced and included resources, as well as a feature that combines all the metadata about the used resources in a 'bag of words'. The action category represents the user interactions and contains features about the interactions with applications [GKS + 08], resources types, resources, key input types (navigational keys, letters, numbers), the number of events and event blocks, the duration of the event blocks, and the time intervals between event blocks. The switching sequences category comprises features about switches between applications, resources as well as event and resource types.

Classifiers and Attribute Selection:

We studied the Naïve Bayes (NB), Linear Support Vector Machine (SVM) with cost parameter c ∈ {2 -5 , 2 -3 , 2 -1 , 2 0 , 2 1 , 2 3 , 2 5 , 2 8 , 2 10 }4 , J48 decision tree (J48) and k-Nearest Neighbor (KNN-k) with k ∈ {1, 5, 10, 35} algorithms. For each classifier/learning algorithm l ∈ L, for each feature category φ ∈ Φ and each feature f ∈ F we selected the g attributes having the highest Information Gain (IG) value to obtain our dataset. As values for g we used 50 different measure points. Half of them were equally distributed over the available number of attributes with an upper bound of 5000 attributes. The other half was defined by G = {3, 5, 10, 25, 50, 75, 100, 125, 150, 175, 200, 250, 300, 500, 750, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 5000, 7500, 10000}. Which attributes are finally used by the classifiers depends on the attribute selection algorithm (IG in our case). To answer our research questions we used the tasks we recorded from the laboratory computer as the training set and those recorded at the personal workstations as the test set. We measured the accuracy (a) of the used algorithms Table 3: Overview of all results about the performance of detecting real workstation tasks by training on CAM from laboratory settings for each feature category, for all feature categories combined, each single feature as well as the k top performing single features. The learning algorithm (l), the number of attributes (g), the micro precision (p), the micro recall (r), the ranking in the corresponding section (RS) and across sections (RG) are also given.

(l), the number of attributes (g), the micro precision (p) and micro recall (r).

Results and Discussion

An overview of all results about the performance of detecting real workstation tasks by training on CAM from laboratory settings is given in Table 3.

Feature Categories: The best feature category was the application category that correctly identified 91.75% of the real tasks (l=NB, g=500, p=0.97, r=0.92). Approximately 5% behind in terms of accuracy was the content category (l=NB, a=86.60%, g=500, p=0.95, r=0.87). Using all 50 features resulted in a 82.47% accuracy, which is about 9% worse than the best performing feature category. This directed our decision to study the used features in greater details.

Single Features: We evaluated the performance of each single feature separately and confirmed that the window title [OSTS06, SLDH06, LFBG07, GKS + 08] was the best dis-criminative feature: it obtained an accuracy of 85.57% (l=J48, g=100, p=0.95, r=0.87). Of great interest are the good performances of accessibility object features: the acc. obj. name with a=80.41% (l=J48, g=100, p=0.92, r=0.81) and the acc. obj. value with a=71.13% (l=J48, g=150, p=0.89, r=0.72). Simply counting the number of UICO datatype relations (a=70.10%) was also quite efficient. Since the performance of the single features were that good we were wondering if we could do better by following the simple approach of combining the k best performing single features with respect to the accuracy (a).

Top k We studied the performance for different k and obtained with the NB classifier at g=250 attributes with the top 6 features the highest accuracy (a=94.85%), precision (p=0.98) and recall (r=0.95), among all studied features, feature categories and top k combinations. This was an accuracy increase of 9.28%, a precision increase of 0.03 and a recall increase of 0.08 compared to the performance of the window title feature.

The number of attributes (250) of this best performing approach also supports prior work showing that a good choice for it is between 200 and 300 attributes [START_REF] Lokaiczyk | Enhancing just-in-time e-learning through machine learning on desktop context sensors[END_REF][START_REF] Shen | A hybrid learning system for recognizing user tasks from desktop activities and email messages[END_REF].

Generalizability to Other CAM Frameworks: CAM frameworks that observe user contextual information differ in terms of utilized sensors and of granularity of the captured CAM. Our approach is very fine-granular since we observe not only the content currently viewed by the user or the window title of the application in focus but also the user's interactions with all desktop elements and application controls (accessibility objects). In our approach every single interaction of the user with an application and a resource is important and hence captured, stored and analyzed. Using a different CAM framework could result in leaving out "context features" with a good task discriminative power and could hence have a negative impact on the task detection performance.

Generalizability to Other Work Contexts:

Our results only give a first impression on the fact that the environment in which users perform their tasks has no significant influence on the task detection performance. Since only four tasks were studied in our experiment, the generalizability of our results is of course limited, and further experiments (with other tasks, other users and in other domains) are needed. However it is well recognized that the window title feature has a good cross-domain discriminative power, and we think that it could be true for other CAM features.

Possible Impacts of our Results: The strong positive influence of specific context features on task detection performance could be an indication that it is not necessary to sense "everything" about the user's interactions with her computer desktop but only some relevant elements. This would have an impact on what kind of sensors have to be developed, i.e. which context features have to be sensed, to achieve a reasonable task detection performance. It would also impact the user's system performance because capturing less data normally leads to less cpu requirements. Furthermore if we know which features are performing well for supervised machine learning algorithms in laboratory settings, it could provide a first indication on which features could be used in an unsupervised learning approach and in real world settings. However, this would require further experiments in laboratory and real world settings.

Following the CAM approach for observing the user's attention seems to be a good choice for automatically detecting the user's task by means of machine learning techniques. We have performed a large-scale experiment that shows that it is possible to obtain good task detection results for real user tasks with a classifier trained offline on laboratory CAM. We also studied the discriminative power of individual and combined CAM features.

The good performance of the classical window title feature was confirmed and even significantly outperformed by a specific combination of 6 features. Within this combination are CAM features that are specific to our ontology-based user interaction context model (UICO). This confirms that our model can improve task detection performance [START_REF] Rath | UICO: an ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF].

We plan to study the discriminative power of our ontology-specific CAM features more thoroughly by performing further experiments with tasks having different characteristics, since the results we have obtained here are maybe domain-specific. We would like to understand why some features perform better than others for task detection. Our objective is to exhibit a small combination of CAM features with a strong discriminative power independently of the domain in order to enhance automatic task detection performance.

Table 1 :

 1 for parts of the data preprocessing, filtering, attribute selection, and classification.Training/Test Instance Construction: Constructing training instances for the machine learning algorithms was done on the task level: each task represents a training instance for a specific class to be learned. A class corresponds to a specific task model. Having multiple task models hence resulted in a multi-class classification problem. An instance for a class was built from features and feature combinations based on the CAM captured plain text) content of currently viewed or sent email, subject, unique path (uri of email/news message) on server, user's mail action (compose, read, send, forward, reply), received/sent time, email addresses and full names of the email entries This table shows a listing of the developed application and system sensors as well as of the data recorded by these sensors. Application sensors are context sensors for standard office applications. System sensors are deep hooks into the operating system. They allow to record user interactions and network transfer data on a fine-granular level.

	Sensor	Observed Data and Metadata
	Application Sensors
	Microsoft Word	document title, document url, language, text encoding, content
			of visible area, file name, folder, user name
	Microsoft Power-	document title, document url, document template name, current
	Point		slide number, language, content, file name
	Microsoft Excel	spreadsheet title, spreadsheet url, worksheet name, content of
			the currently viewed cell, authors, language, file name, file uri,
			folder, user name
	Microsoft Internet	currently viewed url, urls of embedded frames, content as html,
	Explorer		content as plain text
	Microsoft Explorer currently viewed folder/drive name, url of folder/drive path
	Mozilla Firefox 2.x	currently viewed url, urls of embedded frames, content as html
	and 3.x
	Mozilla Thunder-bird (html/Microsoft Outlook (create, delete, modify, open and distribute) tasks, notes, calen-
	2003/2007		dar entries, contacts, data about email handling
	Novell GroupWise	(create, delete, modify, and distribute) tasks, notes, calendar en-
	email client		tries, todos, data about email handling
	System Sensors
	File System Sensor copying from/to, deleting, renaming from/to, moving from/to,
			modification of files and folders (file/folder url)
	Clipboard Sensor	clipboard changes (i.e. text copied to clipboard)
	Network	Stream	header and payload content from network layer packets (http,
	Sensor		ftp, nttp, smtp, messenger, ICQ, Skype. . . )
	Generic Windows	mouse movement, mouse click, keyboard input, window title,
	XP System Sensor	date and time of occurrence, window id/handle, process id, ap-
			plication name
	Accessibility	name, value, description, help text, help text description, tooltip
	Object Sensor	of the accessibility object.

Table 2 :

 2 This table shows the distribution of training and test instances for the different task classes.Training and test instances were constructed based on the usage data recorded on the laboratory computer and on the personal workstations respectively.

For us, CAM frameworks are not only approaches that use the CAM-XML data schema, but more generaly frameworks which observe contextual attention metadata independently of the underlying (sensor) data schema.

It is worth noting that these tasks present different characteristics, in terms of complexity, estimated execution time, number of involved resources, granularity and so on.

Microsoft Active Accessibility: http://msdn.microsoft.com/en-us/accessibility/

The interval was chosen according to the libSVM guide at: http://www.csie.ntu.edu.tw/~cjlin/libsvm/

Acknowledgments

We would like to thank all the people from the Know-Center who participated in the experiment and supported us in carrying out our task experiment study. The Know-Center is funded within the Austrian COMET Program -Competence Centers for Excellent Technologies -under the auspices of the Austrian Ministry of Transport, Innovation and Technology, the Austrian Ministry of Economics and Labor and by the State of Styria. COMET is managed by the Austrian Research Promotion Agency FFG.


Alexandra Antoniouk

Marc Arnaudon

VARIATIONAL PRINCIPLE FOR WEIGHTED POROUS MEDIA EQUATION

may come

Variational principle for weighted porous media equation

Introduction

In the beginning 18th century Leibniz, Maupertuis, Euler claimed that all physical phenomenons may be obtained from the Least Action Principle and since Lagrange and Hamilton it was well understood for the classical mechanics. However only in 1966 V.I. Arnold in [START_REF] Arnold | Sur la géométrie diffŕentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fuides parfaits[END_REF] achieved it for the fluid dynamics. To do this he remarked that the group of volume preserving diffeomorphisms D µ (M ) of a manifold M (µ being a given volume element on M ) is the appropriate configuration space for the hydrodynamics of an incompressible fluid. In this framework the solutions to the Euler equation become geodesic curves with respect to the right invariant metric on D µ , which at g ∈ D µ is given by X

, Y = M < X(x), Y (x) > x dµ(x), for X, Y ∈ T g D µ , < •, • > x is a metric on T x M ,
and µ is the volume element on M induced by the metric. The relation between geodesics on D µ and the Euler equation was further studied in [START_REF] Ebin | MathematicsGroups of Diffeomorphisms and the Motion of an Incompressible Fluid The Annals of Mathematics[END_REF] and shortly may be expressed in the following way. Let t → g t ∈ D µ be a geodesic with respect to the right invariant metric (•, •), v t = d dt g t be the corresponding velocity, and u t = v t • g -1 t be a time dependent vector field on M. Then u t is a solution to the Euler equation for perfect fluid. In particular the map t → g t defined on some time interval [0, T ] minimizes the energy functional

S(g) = 1 2 T 0 M dg t dt 2 dµ(x) dt
and the Euler-Lagrange equations for this functional are precisely the Euler equation for perfect fluid. Developing this approach in [START_REF] Arnaudon | Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability[END_REF], [START_REF] Cipriano | Navier-Stokes equation and diffusions on the group of homeomorphisms of the torus[END_REF], [9], by means of stochastic methods it was

shown that an incompressible stochastic flow g(u) with generator 1 2 ∆+ u t is critical for some energy functional if and only if u solves Navier-Stokes equation for viscous incompressible fluid. See also [START_REF] Constantin | A stochastic Lagrangian representation of the three-dimensional incompressible Navier-Stokes equations[END_REF] and [8] for other stochastic characterizations of solutions to Navier-Stokes equation. The purpose of this article is to show that the weighted porous media equation ( [START_REF] Dolbeault | On the Bakry-Emery criterion for linear diffusions and weighted porous media equations[END_REF], [START_REF] Dolbeault | Lq-Functional inequalities and weighted porous media equations[END_REF]), which generalizes the standard porous media equation, ( 1)

∂u ∂t = -u • ∇ + 1 2 ∆ u q-2 u + ∇P.
1 may be also obtained in the framework of Least Action Principle for specially chosen energy functional. In the particular case of q = 2 this recovers the Navier-Stokes equation.

2.

Operator formulation of variational principle.

For simplicity we work on the torus T of dimension N . From now on, when integrating in the torus, dx will stand for the normalized Lebesgue measure. Definition 2.1. For some smooth divergence free time dependent vector field (t, x) → v t (x) ∈ T x T we define the flow of vt : e t (v) ∈ D µ (T) as a solution of the ordinary differential equation

(2) de t (v) dt = vt (e t (v)), e 0 (v) = I I T .
Let us remark that in some sense e t (v) is a perturbation of identity map in space D µ (T). The solvability of this equation easily follows from the compactness of T and smoothness of v.

Consider a time-dependent divergence-free vector field u on [0, T ] × T. So u takes its values in the tangent bundle of T which can at every point be identified with R N . Divergence-free means that

N j=1 ∂ j u j ≡ 0. Define the operator L(u t ) : C ∞ (T, R N ) → C ∞ (T, R N ) by L(u t )f = 1 2 ∆f + u t • ∇f.
Definition 2.2. The energy functional is defined for q > 1 as

(3) E q (u, v) = 1 q T 0 T ∂ t + L(u t ) e t (v) (e -1 t (v)(x)) q dx dt,
where e -1 t (v) is the inverse map of the diffeomorphism e t (v) : T → T. Definition 2.3. We say that u is a critical point of E q if for all divergence-free time dependent vector field v such that v 0 = 0 and v T = 0, d dε ε=0 E q (u, εv) = 0.

Theorem 2.1. A divergence-free time dependent vector field u is a critical point of E q , q ≥ 2 if and only if there exists a function P (x) such that (1) is satisfied.

Proof. For e t (εv) * u t (x) = T e -1 t (εv)(x) e t (εv) u t e -1 t (εv)(x) , we compute

∂ t + L(u t ) e t (εv) e -1 t (εv)(x) = ε v(t, e -1 t (εv)(x)) + e t (εv) * u t (x) + + 1 2 ∆e t (εv) e -1 t (εv)(x) ,
where T y e t (εv)(•) being the tangent map of e t (εv) at point y. Therefore we have

d dε ε=0 ∂ t + L(u t ) e t (εv) e -1 t (εv)(x) = vt (x) + [u t , v t ](x) + 1 2 ∆v t (x).
Since u t = ∂ t + L(u t ) (I I), for I I = e t (0) : T → T the identity map,

d dε ε=0 E q (u, εv) equals T 0 T ∂ t + L(u t ) (id) q-2 vt + [u t , v t ] + 1 2 ∆v t , u t dx dt = = T 0 T u t q-2 vt + [u t , v t ] + 1 2 ∆v t , u t dx dt.
On the other hand

0 = T u T q-2 u T , v T dx = T 0 T u t q-2 u t , vt + u t q-4 (q -2) < ut , u t > u t + u t q-2 ut , v t dx dt. Therefore, writing u = u t and v = v t , 0 = d dε ε=0 E q (u, εv)+ + T 0 T u q-2 u, v -[u, v], u - ∆v, u 2 + (q -2) u q-4 u, u u, v dx dt.
Due to

T u q-2 < ∇ v u, u > dx = 1 q T < ∇ u q , v > dx = - 1 q T u q div v dx = 0 for div v = 0, we have, using [u, v] = ∇ u v -∇ v u, - d dε ε=0 E q u, (εv) = T 0 T -u q-2 ∇ u v, u - 1 2 v, ∆ u q-2 u + + (q -2) u q-4 u, u u, v + u q-2 u, v dx dt = T 0 T ∇ u u q-2 u - 1 2 ∆ u q-2 u + + (q -2) u q-4 u, u u + u q-2 u, v dx dt = = T 0 T ∂ t + u • ∇ - 1 2 ∆ u q-2 u, v dx dt
(notice that in the second equality we used the fact that T u v, u q-2 dx = T div u v, u q-2 dx = 0). This equality is true for all time dependent divergence free vector field v, so it gives the equivalence between u critical point of E q and solution to equation (1).

Stochastic variational principle for incompressible diffusion flows

We define a diffusion flow g t (x) on T, x ∈ T, t ∈ [0, T ], T > 0 as a stochastic process, which satisfies the Itô stochastic equation:

(4) dg t (x) = σ(g t (x)) dW t + u t (g t (x)) dt, g 0 (x) = x
where u t is a time dependent vector field on T, σ ∈ Γ(Hom(H, T T)) is a C 2 -map satisfying for all x ∈ T (σσ * )(x) = I I TxT , W t is a cylindric Brownian motion in Hilbert space H.

Let us remark that a diffusion flow is a diffusion process {g t (u)(x)} t≥0 with generator L(u t ) = 1 2 ∆ + u t . We define an incompressible diffusion flow g t (u)(x)(ω) as a diffusion flow such that a.s. ω for all t ≥ 0, the map x → g t (u)(x)(ω) is a volume preserving diffeomorphism of T. Examples of incompressible diffusion flows can be found in [START_REF] Cipriano | Navier-Stokes equation and diffusions on the group of homeomorphisms of the torus[END_REF]. Notice that a necessary condition is div u t = 0.

For the diffusion flow g t (4) we define the drift as the time derivative of the finite variation part by Dg t (ω) := u t (g t , ω), and the energy functional by ( 5)

E q (g) := 1 q E T 0 T Dg t (x)(ω) q dx dt , q > 1.
We make a perturbation by letting g v t (u) = e t (v) • g t (u), where v is a smooth divergence free time dependent vector field and e t (v) is defined in (2). Definition 3.1. We say that g t (u) is a critical point for the energy functional E q if for all smooth time dependent divergence free vector field v on T T such that

v 0 = v T = 0, d dε ε=0 E q (g εv (u)) = 0.
Theorem 3.2. Let q ≥ 2. An incompressible diffusion flow g t (u) with generator L(u t ) is a critical point for the energy functional E q if and only if there exists a function P (x) such that u t satisfies equation [START_REF] Arnaudon | Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability[END_REF].

Proof of this theorem is a consequence of Theorem 2.1 and the Itô's formula.

[ 8 ]

 8 G.L. Eyink, Stochastic least action principle for the incompressible Navier-Stokes equations, Phys. D239 (2010), no. 14, 1236-1240. [9] Gliklich Yu. Dep. Nonlinear Analysis Institute of Mathematics NAS Ukraine Tereschchenkivska str, 3 Kyiv, 01 601 UKRAINE E-mail address: antoniouk.a@gmail.com Institut de Mathmatiques de Bordeaux CNRS: UMR 5251 Universit Bordeaux 1 F33405 TALENCE Cedex, France E-mail address: marc.arnaudon@math.u-bordeaux1.fr

Acknowledgements

The research of A.Antoniouk was supported by the grant no. 01-01-12 of National Academy of Sciences of Ukraine (under the joint Ukrainian-Russian project of NAS of Ukraine and Russian Foundation of Basic Research)."

This research was also supported by the French ANR grant ANR-09-BLAN-0364-01 ProbaGeo.


Andreas S Rath

Didier Devaurs

Stefanie N Lindstaedt

HAL is

KnowSe: Fostering User Interaction Context Awareness

Andreas S. Rath, Didier Devaurs, and Stefanie N. Lindstaedt Know-Center GmbH and Knowledge Management Institute, Graz University of Technology, Inffeldgasse 21a 8010 Graz, Austria (arath, ddevaurs, slind)@know-center.at

The CSCW area has recognized the concept of awareness as a critical issue to focus on (Schmidt et al., 2002) since "users who work together require adequate information about their environment" [START_REF] Gross | Awareness in context: A light-weight approach[END_REF]. The environment of an individual encompasses her connections with other people, as well as with digital resources and actions (tasks or processes). If connections are not clear or hidden to the individual or to the group, the cost is a lack of awareness in the organization [START_REF] Mcarthur | Discovery of implicit and explicit connections between people using email utterance[END_REF], which not only leads to inefficient cooperation but can even prevent it from being started. Unveiling the relations between persons, topics, tasks and processes to computer workers facilitates cooperative work by increasing the awareness of the personal social networks and the role of an individual in the organization, a project, or a group. These connections can be created and modeled manually but a better approach is to develop semi-automatic or even automatic tools to create and share them [START_REF] Mcarthur | Discovery of implicit and explicit connections between people using email utterance[END_REF]. Based on emails, [START_REF] Mcarthur | Discovery of implicit and explicit connections between people using email utterance[END_REF] have computed such kind of connections, and suggest using more global corpora as well as taking into account dynamic ones.

We propose an automatic approach [START_REF] Rath | UICO: an ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF] for (i) detecting the interaction context of a single user (i.e. the connections between her tasks, her used digital resources and her social network) and (ii) combining the individual contexts for global awareness. Starting from low-level events captured on the user's desktop about the user's interactions with resources and applications, we utilize rule-based, information extraction and machine learning approaches to automatically derive connections, i.e. relations between our context model's entities. For specifying the types of connections and entities we use an ontology-based context model. By following this semantic technology-based approach we benefit from a well-defined model and specification of the connections; we then gain two advantages for increasing awareness: (i) representing the relations between the user and her close environment (individual view) and (ii) merging multiple individual context models into a global one (organizational view). KnowSe (Knowledge Services) is a service-oriented framework that includes this automatic user interaction context detection as well as the following services for supporting the user's personal and collaborative work:

• Information Need Discovery: These needs can emerge from an active information request (e.g., a search on a web page) or from a change in the user context (e.g., the switch from one task to another).

• Proactive Context-Aware Information Retrieval: Here we focus on utilizing concepts and relations recently added to the individual and organizational context model as a starting point for identifying relevant resources (e.g., people, documents, links, presentations, or folders) via spreading activation on the graph-based representation of the global context model. Furthermore we work on ranking search results (which include resources from personal and organizational knowledge spaces) based on resource usage and interconnectivity. We support user initiated search as well as proactive search.

• Individual and Organizational Context Visualization: For the user to explore her environment from her individual and from the organizational perspective we have developed specific visualization techniques for displaying connections between resources, applications and user actions (graph views), and the usage history of resources in applications within tasks (timeline and selforganizing map views).

Acknowledgments

The Know-Center is funded within the Austrian COMET Program -Competence Centers for Excellent Technologies -under the auspices of the Austrian Federal Ministry of Transport, Innovation and Technology, the Austrian Federal Ministry of Economy, Family and Youth and by the State of Styria. COMET is managed by the Austrian Research Promotion Agency FFG.


Andreas S Rath
email: arath@know-center.at

Didier Devaurs
email: ddevaurs@know-center.at

Stefanie N Lindstaedt

Contextualized Knowledge Services for Personalized Learner Support

In this demonstration we present our KnowSe framework, developed for observing, storing, analyzing and leveraging Contextual Attention Metadata, utilizing our ontology-based user interactions context model (UICO). It includes highly contextualized knowledge services for supporting learners in a personalized and adaptive way, by exploiting the learner's user context.

Personal information management and search systems can be improved by taking into account the context in which information is used and produced by a user, namely the user context. While talking about context we specifically focus here on the information relevant to the interactions of the user with applications and resources (documents, emails, contacts, online content, clipboard content, etc.) on the computer desktop.

Recording the user context is a prerequisite for providing personalized knowledge services. We have thus developed context observation tools (so-called sensors) which record all low-level operating system and application events (keyboard strokes and mouse clicks) initiated by the user while interacting with her desktop [START_REF] Rath | Context-aware knowledge services[END_REF]. For each event, corresponding to a singular interaction of the user with a given application and specific resources, we record all the information relevant to this interaction (window title, date, keyboard input, application name, document or folder name, content of document, etc). Multiple application specific sensors have been developed for Microsoft Office applications, Outlook, Internet Explorer, Mozilla Firefox and Thunderbird.

The contextual information recorded by sensors is sent as an XML stream to the context observation framework for processing and analysis. It is used to automatically populate our User Interaction Context Ontology (UICO) [START_REF] Rath | UICO: An ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF] which constitutes an ontology-based context model of the personal information management domain. This ontology is based on our conceptual model, the semantic pyramid [START_REF] Rath | Context-aware knowledge services[END_REF], in which events are grouped into event-blocks (an event-block representing a sequence of interactions with a given resource) which are themselves grouped into tasks (a task representing a well-defined step of a process involving only one person). This ontology represents a key ingredient of KnowSe, by providing a coherent view on and a single access point to the data, stored in a triple store (more precisely a quad store featuring named graphs and SPARQL query possibilities).

To enhance the information provided by sensors, we use rule-based and information extraction techniques to automatically populate our ontology, by discovering new concepts, and deriving inter-concepts relations [START_REF] Rath | UICO: An ontology-based user interaction context model for automatic task detection on the computer desktop[END_REF]. This allows us to make hidden information and connections between resources and people visible and usable. The UICO is thus constructed iteratively, by considering only the information relevant to the user. The populated UICO can be leveraged for providing the user with personalized and contextualized services.

Context-Aware Information Retrieval Service. Compared to a classical desktop search tool, this service provides further benefits by (i) searching through any kind of resource referenced in the UICO and not only documents, (ii) providing resources from both the personal and the organizational knowledge bases, and (iii) expanding a text-based query with contextual information.

Pro-Active Context-Aware Information Delivery Service. By analyzing the current working context of the user, this service can provide her in real-time with resources relevant to her work. This is done by both (i) expanding text queries and (ii) utilizing concepts and relations recently added to the UICO as a starting point for spreading activation on the graph-based representation of the UICO. Furthermore search results are ranked based on resource usage and inter-connectivity of UICO instances.

User Context Visualization Service. To make the vast amount of information stored in the UICO exploitable by the user we have developed specific visualization techniques for displaying connections between resources, applications and user actions (graph views), as well as the usage history of resources in applications within tasks.

Besides the services we present in this demonstration, we have developed an Information Need Discovery Service, in order to detect and fulfill some user needs. We are also currently developing an Automatic Task Detection Service based on machine learning algorithms (which has already shown a 90% accuracy for task recognition), to be able to support the user with task-based information delivery, task guidance, task automation or task-specific skills training.

A Technical requirements

The demo presenter will bring her own laptop. A good internet connection would be appreciated. If it is known beforehand that this is not possible, local installations of all tools can be made available.

B Target audience

First, we would like to address people who are interested in experiencing how contextual attention metadata about the user's interactions with applications and resources are captured from their own interactions with the computer desktop. Second, we would like to reach researchers who utilize or plan to use user context information to enrich learning management systems in order to enhance the learner's experience. Third, we intend to address experts in the field of contextual attention metadata to show and discuss our ontology-based user context detection approach and its advantages for exploitation in various technology enhanced learning applications.

B.1 Audience Interaction

Our demonstration includes not only a presentation but also allows the audience to interact with our prototype. They are able to walk through the described scenario or create their own ones.

C Demo Storyboard

Our demo storyboard is available online at the following location: http://purl.oclc.org/NET/knowse/ectel2009demo

Acknowledgment The Know-Center is funded within the Austrian COMET Program -Competence Centers for Excellent Technologies -under the auspices of the Austrian Ministry of Transport, Innovation and Technology, the Austrian Ministry of Economics and Labor and by the State of Styria. COMET is managed by the Austrian Research Promotion Agency FFG.