Improved space bounds for strongly competitive randomized paging algorithms
- Paging is one of the prominent problems in the field of on-line algorithms. While in the deterministic setting there exist simple and efficient strongly competitive algorithms, in the randomized setting a tradeoff between competitiveness and memory is still not settled. Bein et al.  conjectured that there exist strongly competitive randomized paging algorithms, using o(k) bookmarks, i.e. pages not in cache that the algorithm keeps track of. Also in  the first algorithm using O(k) bookmarks (2k more precisely), Equitable2, was introduced, proving in the affirmative a conjecture in .
We prove tighter bounds for Equitable2, showing that it requires less than k bookmarks, more precisely ≈ 0.62k. We then give a lower bound for Equitable2 showing that it cannot both be strongly competitive and use o(k) bookmarks. Nonetheless, we show that it can trade competitiveness for space. More precisely, if its competitive ratio is allowed to be (Hk + t), then it requires k/(1 + t) bookmarks.
Our main result proves the conjecture that there exist strongly competitive paging algorithms using o(k) bookmarks. We propose an algorithm, denoted Partition2, which is a variant of the Partition algorithm byMcGeoch and Sleator . While classical Partition is unbounded in its space requirements, Partition2 uses θ(k/ log k) bookmarks. Furthermore, we show that this result is asymptotically tight when the forgiveness steps are deterministic.
Dynamic data structures and saliency-influenced rendering
- With increasing heterogeneity of modern hardware, different requirements for 3d applications arise. Despite the fact that real-time rendering of photo-realistic images is possible using today’s graphics cards, still large computational effort is required. Furthermore, smart-phones or computers with older, less powerful graphics cards may not be able to reproduce these results. To retain interactive rendering, usually the detail of a scene is reduced, and so less data needs to be processed. This removal of data, however, may introduce errors, so called artifacts. These artifacts may be distracting for a human spectator when gazing at the display. Thus, the visual quality of the presented scene is reduced. This is counteracted by identifying features of an object that can be removed without introducing artifacts. Most methods utilize geometrical properties, such as distance or shape, to rate the quality of the performed reduction. This information used to generate so called Levels Of Detail (LODs), which are made available to the rendering system. This reduces the detail of an object using the precalculated LODs, e.g. when it is moved into the back of the scene. The appropriate LOD is selected using a metric, and it is replaced with the current displayed version. This exchange must be made smoothly, requiring both LOD-versions to be drawn simultaneously during a transition. Otherwise, this exchange will introduce discontinuities, which are easily discovered by a human spectator. After completion of the transition, only the newly introduced LOD-version is drawn and the previous overhead removed. These LOD-methods usually operate with discrete levels and exploit limitations of both the display and the spectator: the human.
Humans are limited in their vision. This ranges from being unable to distinct colors at varying illumination scenarios to the limitation to focus only at one location at a time. Researchers have developed many applications to exploit these limitations to increase the quality of an applied compression. Some popular methods of vision-based compression are MPEG or JPEG. For example, a JPEG compression exploits the reduced sensitivity of humans regarding color and so encodes colors with a lower resolution. Also, other fields, such as auditive perception, allow the exploitation of human limitations. The MP3 compression, for example, reduces the quality of stored frequencies if other frequencies are masking it. For representation of perception various computer models exist. In our rendering scenario, a model is advantageous that cannot be influenced by a human spectator, such as the visual salience or saliency.
Saliency is a notion from psycho-physics that determines how an object “pops out” of its surrounding. These outstanding objects (or features) are important for the human vision and are directly evaluated by our Human Visual System (HVS). Saliency combines multiple parts of the HVS and allows an identification of regions where humans are likely to look at. In applications, saliency-based methods have been used to control recursive or progressive rendering methods. Especially expensive display methods, such as pathtracing or global illumination calculations, benefit from a perceptual representation as recursions or calculations can be aborted if only small or unperceivable errors are expected to occur. Yet, saliency is commonly applied to 2d images, and an extension towards 3d objects has only partially been presented. Some issues need to be addressed to accomplish a complete transfer.
In this work, we present a smart rendering system that not only utilizes a 3d visual salience model but also applies the reduction in detail directly during rendering. As opposed to normal LOD-methods, this detail reduction is not limited to a predefined set of levels, but rather a dynamic and continuous LOD is created. Furthermore, to apply this reduction in a human-oriented way, a universal function to compute saliency of a 3d object is presented. The definition of this function allows to precalculate and store object-related visual salience information. This stored data is then applicable in any illumination scenario and allows to identify regions of interest on the surface of a 3d object. Unlike preprocessed methods, which generate a view-independent LOD, this identification includes information of the scene as well. Thus, we are able to define a perception-based, view-specific LOD. Performance measures of a prototypical implementation on computers with modern graphic cards achieved interactive frame rates, and several tests have proven the validity of the reduction.
The adaptation of an object is performed with a dynamic data structure, the TreeCut. It is designed to operate on hierarchical representations, which define a multi-resolution object. In such a hierarchy, the leaf nodes contain the highest detail while inner nodes are approximations of their respective subtree. As opposed to classical hierarchical rendering methods, a cut is stored and re-traversal of a tree during rendering is avoided. Due to the explicit cut representation, the TreeCut can be altered using only two core operations: refine and coarse. The refine-operation increases detail by replacing a node of the tree with its children while the coarse-operation removes the node along with its siblings and replaces them with their parent node. These operations do not rely on external information and can be performed in a local manner. These only require direct successor or predecessor information. Different strategies to evolve the TreeCut are presented, which adapt the representation using only information given by the current cut. These evaluate the cut by assigning either a priority or a target-level (or bucket) to each cut-node. The former is modelled as an optimization problem that increases the average priority of a cut while being restricted in some way, e.g. in size. The latter evolves the cut to match a certain distribution. This is applied in cases where a prioritization of nodes is not applicable. Both evaluation strategies operate with linear time complexity with respect to the size of the current TreeCut.
The data layout is chosen to separate rendering data and hierarchy to enable multi-threaded evaluation and display. The object is adapted over multiple frames while the rendering is not interrupted by the used evaluation strategy. Therefore, we separate the representation of the hierarchy from the rendering data. Due to its design, this overhead imposed to the TreeCut data structure does not influence rendering performance, and a linear time complexity for rendering is retained. The TreeCut is not only limited to alter geometrical detail of an object. The TreeCut has successfully been applied to create a non-photo-realistic stippling display, which draws the object with equal sized points in varying density. In this case the bucket-based evaluation strategy is utilized, which determines the distribution of the cut based on local illumination information. As an alternative, an attention drawing mechanism is proposed, which applies the TreeCut evaluation strategies to define the display style of a notification icon. A combination of external priorities is used to derive the appropriate icon version. An application for this mechanism is a messaging system that accounts for the current user situation.
When optimizing an object or scene, perceptual methods allow to account for or exploit human limitations. Therefore, visual salience approaches derive a saliency map, which encodes regions of interest in a 2d map. Rendering algorithms extract importance from such a map and adapt the rendering accordingly, e.g. abort a recursion when the current location is unsalient. The visual salience depends on multiple factors including the view and the illumination of the scene. We extend the existing definition of the 2d saliency and propose a universal function for 3d visual salience: the Bidirectional Saliency Weight Distribution Function (BSWDF). Instead of extracting the saliency from 2d image and approximate 3d information, we directly compute this information using the 3d data. We derive a list of equivalent features for the 3d scenario and add them to the BSWDF. As the BSWDF is universal, also 2d images are covered with the BSWDF, and the calculation of the important regions within images is possible.
To extract the individual features that contribute to visual salience, capabilities of modern graphics card in combination with an accumulation method for rendering is utilized. Inspired from point-based rendering methods local features are summed up in a single surface element (surfel) and are compared with their surround to determine whether they “pop out”. These operations are performed with a shader-program that is executed on the Graphics Processing Unit (GPU) and has direct access to the 3d data. This increases processing speed because no transfer of the data is required. After computation, each of these object-specific features can be combined to derive a saliency map for this object. Surface specific information, e.g. color or curvature, can be preprocessed and stored onto disk. We define a sampling scheme to determine the views that need to be evaluated for each object. With these schemes, the features can be interpolated for any view that occurs during rendering, and the according surface data is reconstructed. These sampling schemes compose a set of images in form of a lookup table. This is similar to existing rendering techniques, which extract illumination information from a lookup. The size of the lookup table increases only with the number of samples or the image size used for creation as the images are of equal size. Thus, the quality of the saliency data is independent of the object’s geometrical complexity. The computation of a BSWDF can be performed either on a Central Processing Unit (CPU) or a GPU, and an implementation requires only a few instructions when using a shader program. If the surface features have been stored during a preprocess, a reprojection of the data is performed and combined with the current information of the object. Once the data is available, the computation of the saliency values is done using a specialized illumination model, and a priority for each primitive is extracted. If the GPU is used, the calculated data has to be transferred from the graphics card. We therefore use the “transform feedback” capabilities, which allow high transfer rates and preserve the order of processed primitives. So, an identification of regions of interest based on the currently used primitives is achieved. The TreeCut evaluation strategies are then able to optimize the representation in an perception-based manner.
As the adaptation utilizes information of the current scene, each change to an object can result in new visual salience information. So, a self-optimizing system is defined: the Feedback System. The output generated by this system converges towards a perception-optimized solution. To proof the saliency information to be useful, user tests have been performed with the results generated by the proposed Feedback System. We compared a saliency-enhanced object compression to a pure geometrical approach, common for LOD-generation. One result of the tests is that saliency information allows to increase compression even further as possible with the pure geometrical methods. The participants were not able to distinguish between objects even if the saliency-based compression had only 60% of the size of the geometrical reduced object. If the size ratio is greater, saliency-based compression is rated, on average, with higher score and these results have a high significance using statistical tests. The Feedback System extends an 3d object with the capability of self-optimization. Not only geometrical detail but also other properties can be limited and optimized using the TreeCut in combination with a BSWDF. We present a dynamic animation, which utilizes a Software Development Kit (SDK) for physical simulations. This was chosen, on the one hand, to show the universal applicability of the proposed system, and on the other hand, to focus on the connection between the TreeCut and the SDK. We adapt the existing framework, and include the SDK within our design. In this case, the TreeCut-operations not only alter geometrical but also simulation detail. This increases calculation performance because both the rendering and the SDK operate on less data after the reduction has been completed.
The selected simulation type is a soft-body simulation. Soft-bodies are deformable in a certain degree but retain their internal connection. An example is a piece of cloth that smoothly fits the underlying surface without tearing apart. Other types are rigid bodies, i.e. idealistic objects that cannot be deformed, and fluids or gaseous materials, which are well suited for point-based simulations. Any of these simulations scales with the number of simulation nodes used, and a reduction of detail increases performance significantly. We define a specialized BSWDF to evaluate simulation specific features, such as motion. The Feedback System then increases detail in highly salient regions, e.g. those with large motion, and saves computation time by reducing detail in static parts of the simulation. So, detail of the simulation is preserved while less nodes are simulated.
The incorporation of perception in real-time rendering is an important part of recent research. Today, the HVS is well understood, and valid computer models have been derived. These models are frequently used in commercial and free software, e.g. JPEG compression. Within this thesis, the Tree-Cut is presented to change the LOD of an object in a dynamic and continuous manner. No definition of the individual levels in advance is required, and the transitions are performed locally. Furthermore, in combination with an identification of important regions by the BSWDF, a perceptual evaluation of a 3d object is achieved. As opposed to existing methods, which approximate data from 2d images, the perceptual information is directly acquired from 3d data. Some of this data can be preprocessed if necessary, to defer additional computations during rendering. The Feedback System, created by the TreeCut and the BSWDF, optimizes the representation and is not limited to visual data alone. We have shown with our prototype that interactive frame rates can be achieved with modern hardware, and we have proven the validity of the reductions by performing several user tests. However, the presented system only focuses on specific aspects, and more research is required to capture even more capabilities that a perception-based rendering system can provide.
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria
- This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012),
to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination
is to be a venue for presentation and discussion of all topics in and around termination. In this way,
the workshop tries to bridge the gaps between different communities interested and active in research
in and around termination. The 12th International Workshop on Termination in Obergurgl continues
the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999),
Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and
The 12th International Workshop on Termination did welcome contributions on all aspects of termination
and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming
communities, and papers investigating applications of complexity or termination (for example in
program transformation or theorem proving) were particularly welcome.
We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In
addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto.
Encoding induction in correctness proofs of program transformations as a termination problem
- The diagram-based method to prove correctness of program transformations consists of computing
complete set of (forking and commuting) diagrams, acting on sequences of standard reductions
and program transformations. In many cases, the only missing step for proving correctness of a
program transformation is to show the termination of the rearrangement of the sequences. Therefore
we encode complete sets of diagrams as term rewriting systems and use an automated tool
to show termination, which provides a further step in the automation of the inductive step in
Correctness of an STM Haskell implementation
- A concurrent implementation of software transactional memory in Concurrent Haskell using a call-by-need functional language with processes and futures is given. The description of the small-step operational semantics is precise and explicit, and employs an early abort of con
icting transactions. A proof of correctness of the implementation is given for a contextual semantics with may- and should-convergence.
This implies that our implementation is a correct evaluator for an abstract specification equipped with a big-step semantics.
Simulation in the call-by-need lambda-calculus with letrec, case, constructors, and seq
- This paper shows equivalence of applicative similarity and contextual approximation, and hence also of bisimilarity and contextual equivalence, in LR, the deterministic call-by-need lambda calculus with letrec extended by data constructors, case-expressions and Haskell's seqoperator. LR models an untyped version of the core language of Haskell. Bisimilarity simplifies equivalence proofs in the calculus and opens a way for more convenient correctness proofs for program transformations.
The proof is by a fully abstract and surjective transfer of the contextual
approximation into a call-by-name calculus, which is an extension
of Abramsky's lazy lambda calculus. In the latter calculus equivalence
of similarity and contextual approximation can be shown by Howe's
method. Using an equivalent but inductive definition of behavioral preorder
we then transfer similarity back to the calculus LR.
The translation from the call-by-need letrec calculus into the extended call-by-name lambda calculus is the composition of two translations. The first translation replaces the call-by-need strategy by a call-by-name strategy and its correctness is shown by exploiting infinite tress, which emerge by unfolding the letrec expressions. The second translation encodes letrec-expressions by using multi-fixpoint combinators and its correctness is shown syntactically by comparing reductions of both calculi. A further result of this paper is an isomorphism between the mentioned calculi, and also with a call-by-need letrec calculus with a less complex definition of reduction than LR.
Cellular and nuclear morphology…and calcium signaling: revealing the interplay between structure and function
Peter von der Bengtson
- Poster presentation: Calcium plays a pivotal role in relaying electrical signals of the cell to subcellular compartments, such as the nucleus. Since this one ion type is used by the cell for many processes a neuron needs to establish finely tuned calcium pathways in order to be able to differentiate multiple tasks, [1-3].
While it is known that neurons can actively change their shape upon neuronal activity, [4-7], we here present novel findings of activity-regulated nuclear morphology, [8,9]. With the help of an experimental and computational modeling approach, we show that hippocampal neurons can change the previously spherical shape of their nuclei to complex and infolded morphologies. This morphology regulation is demonstrated to be regulated by NMDA-receptor gated calcium, while synaptic and extra-synaptic NMDA-receptors elicit opposing effects on nuclear morphology, .
The structural alterations of the cell nucleus have significant effects on nuclear calcium dynamics. Compartmentalization of the nucleus, due to membrane infoldings, changes calcium frequencies, amplitudes and spatial distributions, [8,10]. Since these parameters have been shown to control downstream events towards gene transcription, [11,12], the results elucidate the cellular control of nuclear function with the help of morphology modulation. With respect to processes downstream of calcium, we show that histone H3 phosphorylation is closely linked to nuclear morphology. Investigating the nuclear morphologies of hippocampal neurons, two major classes were identified [9,10]. One class contains non-infolded nuclei that have the function of calcium signal integrators, while the other class contains highly infolded nuclei, which function as frequency detectors of nuclear calcium, .
Extending this interdisciplinary approach of investigating structure/function relationships in neurons, the effects of cellular morphology – as well as the morphology of the endoplasmic reticulum and other organelles – on neuronal calcium signals is currently being investigated. This endeavor makes use of highly detailed, three-dimensional models of neuronal calcium dynamics, including the three-dimensional morphology of the cell and its organelles.
Conceptual design of an ALICE Tier-2 centre integrated into a multi-purpose computing facility
- This thesis discusses the issues and challenges associated with the design and operation of a data analysis facility for a high-energy physics experiment at a multi-purpose computing centre. At the spotlight is a Tier-2 centre of the distributed computing model of the ALICE experiment at the Large Hadron Collider at CERN in Geneva, Switzerland. The design steps, examined in the thesis, include analysis and optimization of the I/O access patterns of the user workload, integration of the storage resources, and development of the techniques for effective system administration and operation of the facility in a shared computing environment. A number of I/O access performance issues on multiple levels of the I/O subsystem, introduced by utilization of hard disks for data storage, have been addressed by the means of exhaustive benchmarking and thorough analysis of the I/O of the user applications in the ALICE software framework. Defining the set of requirements to the storage system, describing the potential performance bottlenecks and single points of failure and examining possible ways to avoid them allows one to develop guidelines for selecting the way how to integrate the storage resources. The solution, how to preserve a specific software stack for the experiment in a shared environment, is presented along with its effects on the user workload performance. The proposal for a flexible model to deploy and operate the ALICE Tier-2 infrastructure and applications in a virtual environment through adoption of the cloud computing technology and the 'Infrastructure as Code' concept completes the thesis. Scientific software applications can be efficiently computed in a virtual environment, and there is an urgent need to adapt the infrastructure for effective usage of cloud resources.
Development of cue integration with reward-mediated learning
- This thesis will first introduce in more detail the Bayesian theory and its use in integrating multiple
information sources. I will briefly talk about models and their relation to the dynamics of an environment,
and how to combine multiple alternative models.
Following that I will discuss the experimental findings on multisensory integration in humans and
animals. I start with psychophysical results on various forms of tasks and setups, that show that the brain
uses and combines information from multiple cues. Specifically, the discussion will focus on the finding
that humans integrate this information in a way that is close to the theoretical optimal performance.
Special emphasis will be put on results about the developmental aspects of cue integration, highlighting
experiments that could show that children do not perform similar to the Bayesian predictions. This section
also includes a short summary of experiments on how subjects handle multiple alternative environmental
dynamics. I will also talk about neurobiological findings of cells receiving input from multiple receptors
both in dedicated brain areas but also primary sensory areas.
I will proceed with an overview of existing theories and computational models of multisensory integration.
This will be followed by a discussion on reinforcement learning (RL). First I will talk about the
original theory including the two different main approaches model-free and model-based reinforcement
learning. The important variables will be introduced as well as different algorithmic implementations.
Secondly, a short review on the mapping of those theories onto brain and behaviour will be given. I mention
the most in
uential papers that showed correlations between the activity in certain brain regions
with RL variables, most prominently between dopaminergic neurons and temporal difference errors. I
will try to motivate, why I think that this theory can help to explain the development of near-optimal
cue integration in humans.
The next main chapter will introduce our model that learns to solve the task of audio-visual orienting.
Many of the results in this section have been published in [Weisswange et al. 2009b,Weisswange
et al. 2011]. The model agent starts without any knowledge of the environment and acts based on predictions
of rewards, which will be adapted according to the reward signaling the quality of the performed
action. I will show that after training this model performs similarly to the prediction of a Bayesian
observer. The model can also deal with more complex environments in which it has to deal with multiple
possible underlying generating models (perform causal inference). In these experiments I use di#erent
formulations of Bayesian observers for comparison with our model, and find that it is most similar to
the fully optimal observer doing model averaging. Additional experiments using various alterations to
the environment show the ability of the model to react to changes in the input statistics without explicitly
representing probability distributions. I will close the chapter with a discussion on the benefits and
shortcomings of the model.
The thesis continues whith a report on an application of the learning algorithm introduced before
to two real world cue integration tasks on a robotic head. For these tasks our system outperforms a
commonly used approximation to Bayesian inference, reliability weighted averaging. The approximation
is handy because of its computational simplicity, because it relies on certain assumptions that are usually
controlled for in a laboratory setting, but these are often not true for real world data. This chapter is
based on the paper [Karaoguz et al. 2011].
Our second modeling approach tries to address the neuronal substrates of the learning process for cue integration. I again use a reward based training scheme, but this time implemented as a modulation of
synaptic plasticity mechanisms in a recurrent network of binary threshold neurons. I start the chapter
with an additional introduction section to discuss recurrent networks and especially the various forms of
neuronal plasticity that I will use in the model. The performance on a task similar to that of chapter 3 will be presented together with an analysis of the in
uence of different plasticity mechanisms on it.
Again benefits and shortcomings and the general potential of the method will be discussed.
I will close the thesis with a general conclusion and some ideas about possible future work.
Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)