Transport Protocols for Wireless Sensor Networks: State-of-the-Art and Future Directions Characteristics of wireless sensor networks, specifically dense deployment, limited processing power, and limited power supply, provide unique design challenges at the transport layer. Message transmission between sensor nodes over a wireless medium is especially expensive. Care must be taken to design an efficient transport layer protocol that combines reliable message delivery and congestion control with minimal overhead and retransmission. Sensor networks are created using low cost, low power nodes. Wireless sensors are assumed to have a finite lifetime; care must be taken to design and implement transport layer algorithms that allow maximum network lifetime. In this paper we present current and future challenges in the design of transport layers for sensor networks. Current transport layer protocols are compared based on how they implement reliable message delivery, congestion control, and energy efficiency. Wireless sensor networks (WSNs) provide a powerful means to collect information on a wide variety of natural phenomena. WSNs typically consist of a cluster of densely deployed nodes communicating with a sink node which, in turn, communicates with the outside world. WSNs are constrained by low power, dense deployment, and limited processing power and memory. WSNs are composed of small, cheap, self-contained, and disposable sensor nodes. The unique constraints imposed by WSNs present unique challenges in the design of such networks.. The need for a transport layer to handle congestion and packet loss recovery in WSNs has been debated; the idea of a cheap, easily deployable network runs contrary to the costly, lengthy process of implementing a unique and specialized transport layer for a WSN. WSNs have advanced to the level of specialization where congestion control and reliability can be incorporated at each individual node.. Reliable data transmission in WNSs is difficult due to the following characteristics of WSNs:. • limited processing capabilities and transmission range of sensor nodes;. • close proximity to ground causes signal attenuation or channel fading which leads to asymmetric links; • close proximity to ground and variable terrain also leads to shadowing which can effectively isolate nodes from the network; • conservation of energy requires unused nodes and wake only when needed;. • dense deployment of sensor nodes creates significant channel contention and congestion. A transport layer is needed in wireless sensor networks to control congestion and ensure reliable delivery of messages from the sensor nodes to the sink. The limited energy, memory, and computational resources of sensor nodes require an energy-efficient transport layer. Traditional transport protocols, such as TCP/IP, do not provide an efficient enough alternative without serious modification; however, modifying TCP/IP may prove useful at sink nodes to optimize communication between regions in the sensor fields and hosts on foreign networks.. More research is needed on congestion control in sensor networks. A measure of data "goodness" to supplement a protocol, such as ESRT, may be beneficial in determining whether a data needs to be retransmitted. If the current aggregated data at a node does not measure up to the goodness level, the node could hold the data until more neighbors report information to be aggregated, thereby reducing the amount of data repeated on the network. Sliding granularity protocol is another area of future research. A protocol similar to ESRT, that when notified of an event, dynamically shifts granularity so that messages can be watched more closely. This way protocols such as RMST or PSFQ that provide reliability based off a negative acknowledgement system would not have to account for the overhead of sending NACKs unless some event has been sensed.

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


On the Expressiveness of Implicit Provenance in Query and Update Languages Information concerning the origin of data (that is, its provenance) is important in many areas, especially scientific recordkeeping. Currently, provenance information must be maintained explicitly, by added effort of the database maintainer. Since such maintenance is tedious and error-prone, it is desirable to provide support for provenance in the database system itself. In order to provide such support, however, it is important to provide a clear explanation of the behavior and meaning of existing database operations, both queries and updates, with respect to provenance. In this paper we take the view that a query or update implicitly defines a provenance mapping linking components of the output to the originating components in the input. Our key result is that the proposed semantics are expressively complete relative to natural classes of queries that explicitly manipulate provenance. The provenance of data -its origins and how it came to be included in a database -has recently sparked some research interest [4, 12, 14] . The topic is particularly important in those scientific databases, sometimes referred to as curated databases, that are constructed by a labor-intensive process of copying, correcting and annotating data from other sources. The value of curated databases lies in their organization and in the trustworthiness of their data. Provenance is particularly important in assessing the latter. In practice, provenance -if it is recorded at all -is recorded manually, which is both time-consuming and errorprone. Automated provenance recording support is desirable, and for this it is essential to have a proper semantic foundation to guide us on what should be recorded and to understand what effect database operations have on provenance.. We focus on a specific kind of provenance associated with the copying and modification of data by query and update languages. We use a formalization based on the "tagging" or "propagation" approach of Wang and Madnick [15] and Bhagwat et al. [3] . In this approach, it is assumed that each input data item has an identifying color. Existing database operations are then given a new semantics as functions mapping such colored databases to colored databases in which colors are propagated along with their data item during computation of the output. The provenance of a data item in the output is then simply that input data item with the same color. To illustrate this approach, consider a table R(A, B) with tuples {(1, 2), (8, 9 )}, and consider the following SQL query.. (select * from R where A <> 1) union (select A, 5 as B from R where A = 1) (a). The input tree at the left of Fig. 1 is a representation of R in which the atomic data values, the tuples and the table R itself are all annotated with colors c 1 , c 2 , . . .. We could then define the colored semantics of query (a) to map the input to the colored table represented by the tree (a) in Fig. 1 . This defines the provenance of the atom 1 in the output to be the corresponding atom in R, the provenance of the tuple (8, 9) to be the second tuple in R, and so on. The color ⊥ indicates that a data item is introduced by the query itself. Hence, this particular colored semantics takes the view that queries construct new tables and that the second select subquery constructs a new tuple rather than copying an existing one. Color-propagating functions from colored databases to colored databases can hence be used to formally define the provenance behavior of existing database operations. By "color-propagating" we mean that the function should only use colors to indicate the origin of output items: if the function is applied to a recolored version of the input, then it should produce an output with the same recoloring applied. In particular, the input colors cannot influence the uncolored part of the output and the function's behavior is insensitive to the actual choice of colors used in the input. We shall refer to such propagating functions as provenance-aware operations.. The particular provenance ascribed to query (a) in Fig. 1 has the property that if an output item j has the same color as an input item i, then i and j are identical. We shall call provenance-aware operations with this property copying. A copying operation has the property that if some item is colored ⊥ ("blank"), all items that contain it will also be colored ⊥.. The provenance of query (a) described in Fig. 1 is exactly the "intuitive" or "default" provenance of SQL queries proposed by Bhagwat et al. [3] , although they only consider provenance of atomic values. In particular, the default provenance is always copying, as it views constant and tuple constructors in queries as creating new items. Of course, this default semantics may not be the provenance semantics that a curator wants to give to a particular query. For this reason, [3] proposes an extension to query languages that allows provenance to be defined explicitly. Our first result is to propose a default provenance semantics for query languages, similar to that given in [15] and [3] , and show that it is complete in the sense that it expresses exactly the explicitly definable provenance-aware operations that are copying. This shows that the default provenance semantics is a reasonable semantics for queries.. Turning to updates, we note that simple update languages, such as the expressions of SQL that modify data, do not express more database transformations than do SQL queries, and they have been largely ignored in database theory. However, the following examples show that the story is very different when we take account of provenance.. Since updates do not construct new databases, but modify existing ones inplace, it is reasonable to define their provenance semantics in a way that agrees with how tuple identifiers are preserved in practical database management systems. For example, the provenance of updates (b) and (c) would behave on R as illustrated in Fig. 1(b) and Fig. 1(c) , respectively. Note that this provenance semantics is no longer copying. For example, the provenance of the tuple (1, 5) in Fig. 1(b) is the tuple (1, 2) from the input, although they are clearly not identical. For this reason we introduce a weaker semantic restriction on provenance-aware operations, and consider the kind-preserving ones. By "kind-preserving" we mean that if output item j has the same color as input item i, then they are of the same kind: they are both sets, both tuples, or identical atoms. Kind-preserving operations allow the output type of an item to differ from its input type, and this is practically important in considering operations such as SQL's add column update, which extends a tuple but does not change its provenance. We propose a default provenance semantics for updates as kind-preserving operations, and show this semantics to be complete in the sense that every explicitly definable kind-preserving provenance-aware operation can be expressed by the default provenance semantics of an update.. Most previous work on provenance focuses on the relational model. We shall work in the more general "nested relational" or complex object data model [1, 7] for two reasons. First, as our examples indicate, we are interested in provenance at all levels: atoms, tuples, and tables (sets of tuples); a complex object model allows us to provide a uniform treatment of these levels. Second, complex object models are widely used in scientific data, where provenance is of paramount importance. Liefke and Davidson [11] proposed a simple and elegant language that extends SQL-style updates to complex objects. To be more precise about our completeness result for updates: it is the default provenance of this language that we show complete with regard to the explicitly definable, kind-preserving provenance-aware operations. It is therefore a natural choice for updating complex-object databases when one wants to record provenance.. Related work. There is a substantial body of research on provenance (sometimes termed lineage or pedigree) in both database and scientific computing settings, which is nicely surveyed in [4, 12, 14] . In early approaches to provenance [15, 8] the provenance of an output tuple consists of sets of input tuples that directly or indirectly influenced the output. These techniques only track the provenance of tuples in relational data. In [6] a distinction is made between "why" and "where" provenance for queries in a tree-structured model. More recently, [5] investigated tracking where-provenance for manual updates to curated databases. The Trio project [2] has investigated the combination of tuple-level lineage with uncertainty and accuracy information.. There has also been significant work on the properties of "tagging" or "annotation" in databases. Tan [13] studied theoretical issues of query containment and equivalence in the presence of annotations. The DBNotes system [3] uses variations on why-and where-provenance to propagate annotations on source data through queries. Geerts et al. have developed Mondrian [10] , a database system that supports block annotations, in which a color can be associated with a subset of the fields in a table, not just a single value.. Finally, provenance has also been studied in the geospatial and Grid computing communities [4, 9, 12] . Here, the motivation is to record the workflow that constructs large data sets in order to avoid repeated computation.

O O O O O B O O O O B O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Communities of everyday practice and situated elderliness as an approach to co-design for senior interaction In the co-design project Senior Interaction a public care unit, university researchers, industrial partners, and senior citizens are working together to design living labs applying digital concepts that can strengthen social networks and interaction among seniors. When approaching people who we envisioned to be the future users we realized that almost nobody among the people between 55 and 75 years old identified themselves as 'elderly' or 'senior citizens', we realized that users are never just 'out there'. Instead they tend to refer to 'the others' or even to their own parents. Rather than using biological age, institutional categories or similar formal ways to group the people that we imagine as the future users, we suggest to talk about situated elderliness. By associating elderliness not to all encompassing life circumstances but to certain everyday contexts we can turn our attention towards what we call communities of everyday practice that defines these contexts. This paper reflects on issues relating to recruiting and engaging senior people as users in a co-design project. In the Senior Interaction project a public care unit, two universities, nine private companies and senior citizens collaborate to design concepts that can strengthen social interaction among seniors in a specific urban environment. The overall objective is to develop and explore welfare technologies and service models that support experiences and social interaction among seniors and thus contributing to greater self-reliance and social wellbeing. The project suggests a move away from service models focusing on a relation between the individual citizen and the service provider towards concepts based on a broader content and social perspective offering opportunities for peer-to-peer communication closely connected to ongoing everyday activities. Focus is on initiating and maintaining locally based networks by offering services to groups of seniors for instance in relation to the meal, exercise and mobility, and cultural experiences. These areas seems to have a great potential of binding people together in a neighborhood and thus contribute to the feeling of belonging and being confident in the local environment. When the Senior Interaction co-project started we did not know that recruiting seniors already in the initial steps should prove to be so complicated. Our project wants to expose a vivid senior culture spanning the 55 year old just getting to the point of considering that she is in the second part of life and the 93 year old at an elderly care home realizing that life is coming to an end. We may have started out naively assuming that our co-designers are already there ready to embark on our project journey. But constructing who are to be considered as future users is part of the effort. During the initial visits to social clubs, elderly homes and community centers "We are not.." seem to be much more the statements than " yes we are..". Our project seems to depend on a particular definition of being a senior that were much too simplified and stereotype. Rather than using biological age, institutional categories or similar formal ways to group the users that we imagine as the future users, we suggest therefore to talk about situated elderliness. We acknowledge that the rationale of our project is to address and assist citizens in coping with the particular circumstances of for example reduced mobility and potential social isolation associated with becoming elderly. By associating such elderliness not to all encompassing life circumstances but to certain everyday contexts we can turn our attention towards the communities of practice that defines these contexts. When reflecting on our process of recruiting and engaging senior participants as potential users in the project it seems that what we actually did was inviting groups of people sharing some kind of everyday practices to the workshops.

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


On periodicity of generalized two-dimensional infinite words A generalized two-dimensional word is a function on Z 2 with a finite number of values. The main problem we are interested in is periodicity of twodimensional words satisfying some local conditions. Let A be a matrix of order n. The function ϕ : Z , where for x = (x 1 , x 2 ), y = (y 1 , y 2 ) we have |y − x| = |y 1 − x 1 | + |y 2 − x 2 |. We prove that every generalized centered function of radius r > 1 with a finite number of values is periodic. For r = 1 the existence of non-periodic generalized centered functions depends on the spectrum of the matrix A. Similar results are obtained for the infinite triangular and hexagonal grids. The study of local conditions ensuring periodicity is an important problem for the combinatorics on words, both in the 1-dimensional and 2-dimensional case. One of the principle results of combinatoric on words, the Critical Factorization Theorem, relates local periodicities of a word to its global periodicity. It was first proved by Cesari and Vincent, and in the present form it is due to Duval [3, 5] . Connections between local and global periodicity are studied well, see also [11, 9] and [7] for a multidimensional extension.. Some questions about periodicity become much more difficult in dimensions higher than one. One of such questions is the connection between local complexity and periodicity. For a k-dimensional word ω its complexity function p ω (n 1 , . . . , n k ) counts the number of distinct n 1 × . . . × n k blocks in ω. In the one-dimensional case it is known that if there exist an integer n such that p ω (n) ≤ n, then ω is periodic (Morse, Hedlund [10] ). For k = 2 the following hypothesis is known as Nivat's conjecture [12] : if there exists a pair (n, m) such that the complexity function p ω (n, m) of a two-dimensional word ω satisfies the condition p ω (n, m) ≤ mn, then ω has at least a periodicity vector. Weak forms of the conjecture for p ω (n, m) ≤ mn/144 and for p ω (n, m) ≤ mn/16 were proved by C. Epifanio, M. Koskas, F. Mignosi in [6] and by A. Quas, L. Zamboni in [17] , respectively. In [2] V. Berthe, L. Vuillon explore the notion of minimal complexity for two-dimensional sequences, in particular, they give an example of two-dimensional sequence of complexity p ω (n, m) = mn + m, for every (m, n), which is uniformly recurrent and which has no rational periodic direction.. We consider some special types of two-dimensional words as functions on vertices of the graphs of the infinite rectangular, triangular and hexagonal grids. Let G = (V, E) be a graph. The distance between two vertices x and y, denoted by d(x, y), is the usual graph metric, i.e. the number of edges in the shortest path connecting these vertices. A ball B r (x) of radius r with the center at the vertex x is defined in the following way: B r (x) = {y ∈ V | d(x, y) ≤ r}.. Let A = (a ij ) Notice that if n = 1, then A is an eigenvalue of the graph G and generalized centered function is an eigenvector corresponding to eigenvalue A. [4] In fact, the notion of a generalized centered function is a generalization of the notions of a perfect coloring and of an ordinary centered function. A coloring of the graph G into n colors is a function f : V → {1, .., n}. Let A = (a ij ) n i,j=1 be an integer nonnegative matrix, r an integer, r ≥ 1. A coloring of vertices of a graph G with n colors is called perfect of radius r with the matrix A, if for every vertex of a color i the number of vertices of a color j at distance at most r from the vertex of a color i does not depend on the vertex and is equal to a ij . A perfect coloring with n colors with the matrix A can be considered as a generalized centered function with the value area {e 1 , · · · , e n }, where e i is a unit vector with 1 in its i-th coordinate. The notion of perfect coloring naturally arises in different fields of mathematics, such as algebraic combinatorics, graph theory and coding theory. Properties of perfect colorings had been studied under different names, e. g. equitable partitions (see, for example, [8] ).. A function f : V (G) → R is called centered of radius r if the sum of its values in every ball of radius r is equal to 0. An ordinary centered function can be considered as a generalized centered function for n = 1, A = −1. The notion of a centered function was introduced as a generalization of the notion of a perfect code in the hypercube H n [1] . The notion of a perfect coloring also generalizes the notion of a perfect code and several other well-known codes, such as the Preparata code, a completely regular code, a uniformly packed code. Namely, these codes can be interpreted as perfect colorings into two or more colors. This means that generalized centered functions can be used as an instrument for studying perfect colorings and different codes.. In this paper the periodicity of generalized centered functions is studied. In the one-dimensional case generalized centered functions are periodic, the question is non-trivial in dimensions higher than 1. We prove that every generalized centered function of radius r > 1 with a finite number of values on the infinite rectangular grid is periodic. For r = 1, generalized centered function with the matrix A such that det A = 0 is also periodic. If r = 1 and det A = 0, then there exist non-periodic and periodic generalized centered functions. Similar results are obtained for the infinite triangular and hexagonal grids. These results are obtained using the method of R-prolongable words, which had been earlier used for obtaining some results about periodicity of perfect colorings and ordinary centered functions [16] , [13] , [14] .. The results of this paper generalize some previous results, present them in new general notation and explain them in a convenient linear-algebraic form. The property of periodicity in different meanings have been studied for a long time. There exist many methods of proving periodicity and many theorems about periodicity of different types of words. In this paper we develop the method of R-prolongable words for proving periodicity of words with local conditions. The results of this paper can be summarized in the following table. In each cell we write necessary and sufficient conditions for existence of nonperiodic functions in the corresponding case. We suppose that the technique used for graphs of these grids can be also used for other transitive graphs, because the notion of R-prolongability and Lemma 1 can be generalized for this case.. For example, consider a group H =< a , .., a n ) is periodic? Notice that the triangular grid can be interpreted as a Cayley graph G ((1, 0), (0, 1), (1, 1) ). It would be interesting to consider the periodicity of m-dimensional words of this type.

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


Hardness of robust network design The authors settle the complexity status of the robust network design problem in undirected graphs. The fact that the flow-cut gap in general graphs can be large, poses some difficulty in establishing a hardness result. Instead, the authors introduce a single-source version of the problem where the flow-cut gap is known to be one. They then show that this restricted problem is coNP-Hard. This version also captures, as special cases, the fractional relaxations of several problems including the spanning tree problem, the Steiner tree problem, and the shortest path problem. A crucial assumption in many network design problems is that of knowing the traffic demands in advance. Unfortunately, measuring and predicting traffic demands are difficult problems. Moreover, in several applications, communication patterns change over time, and therefore we are not given a single static traffic demand, but instead a set of nonsimultaneous traffic demands. The network should be able to support any traffic demand that is from the given set.. In this paper, we consider the following robust network design problem. We are given a graph G = (V , E) on n nodes and a convex body P D of n×n non-negative "demand" matrices. We work primarily with undirected graphs, although our main result holds also in the directed setting. We denote by U(P D ) the set of all capacity reservations in G that support every demand matrix D ∈ P D . We make this more precise now.. An instance will be called oriented if a demand between a pair of nodes i, j is distinguished by whether it starts at node i, or at node j. Otherwise, it is called unoriented; in this case, D is a symmetric matrix where, for each i, j, the entries D ij = D ji represent the same single demand between i, j. For instances where G is a directed graph, all demands are necessarily oriented since they must be routed on directed paths from i to j. However, in undirected graphs, demands may be oriented or unoriented. Thus, we allow demand matrices D to be asymmetric even in undirected graphs, and, in this case, D ij and D ji identify distinct demands starting from i and j, respectively. We work now in this oriented setting as it is more general; for instance, one can work with lower triangular matrices to mimic unoriented demands.. We now define the region U(P D ). Let P ij denote the finite set of simple paths between i and j. (In principle, we could also define P ij to only be a subset of such paths which are "feasible" for the demand from i to j.) An edge capacity reservation u : E → R + is in U(P D ) (for oriented demands) if for each D ∈ P D and for each ordered pair ij, there is an assignment f ij P of flows to paths P in G such that for each ij: P∈P ij f ij P = D ij and for each edge e ∈ E: ij P∈P ij :e∈P f ij P ≤ u e . We call the assignment f a feasible flow for the demands D. Note that U(P D ) is convex. Given a cost vector c, our aim is to find a vector u ∈ U(P D ) that minimizes cu. In this note, we settle the complexity of robust network design, by establishing its coNP-hardness, even when P D is given by a set of explicit constraints whose size is polynomial in n. To our knowledge, this problem was first suggested in [4] ; moreover, an O(log n) approximation can be obtained (Gupta, personal communication, 2004) .. We emphasize that, in our model, the routing can vary as the traffic demand changes. The same hypothesis has been implicitly considered for a robust network design problem in a recent paper [22] , where the objective is to minimize an appropriate measure of the set of the unsatisfied demands; the authors propose a cutting-plane algorithm for the special case in which P D is the convex hull of a discrete number of scenarios.. Related work has addressed oblivious routing, which is sometimes also referred to as stable routing. The routing is oblivious in the sense that a common routing template is used for each relevant traffic demand matrix. More precisely, for each ordered pair of nodes ij (or unordered pair {i, j} in some contexts), the routing specifies a unit flow: if D ij demand needs to be routed for some traffic matrix D ∈ P D , then it simply scales the unit flow by D ij . The robust network design problem with oblivious routing is considered in [4] , where a column-generation algorithm is studied. An introduction to the use of polytopes for modeling traffic demand, under an oblivious routing template, is given in [5] . The authors also suggest a period-dependent routing as an intermediate strategy between oblivious routing and fully dynamic routing, owing to the inherent impracticalities to implement the latter.. Another line of work seeks oblivious routings that minimize congestion. More precisely, suppose we are given network G with a capacity reservation u : E → R + . A (not necessarily feasible) flow is said to have congestion α if it becomes feasible after scaling up each capacity by a factor of α. A congestion bound for a routing template (i.e., for an oblivious routing) is a value β such that if a demand matrix D can be routed by some flow with congestion α, then routing D using the template has a congestion of at most αβ. For undirected graphs, Räcke [24] showed the existence of oblivious routings with a congestion bound that is polylogarithmic in n. In [2, 3] algorithms are given (both for directed and undirected graphs) to find oblivious routings with optimal congestion bounds. One may formulate this problem of finding an oblivious routing, with a minimum congestion bound, as a robust network optimization problem as follows. Let P D be the set of traffic matrices that can be routed in G with congestion at most 1. We may restrict to these matrices since for any value a > 1, if a flow f routes a matrix D with congestion β, then the flow (1/a)f routes the matrix (1/a)D with congestion β. Hence a routing template has a congestion bound of β if routing every demand matrix D ∈ P D , using the template, has a congestion of at most β. Thus the problem is to find a minimum β for which there is a routing template such that each demand matrix in P D is routed obliviously using capacity at most βu e for each edge e. In [3] , a polynomial time algorithm based on the ellipsoid algorithm is given for this problem. In [2] another algorithm is given by formulating the problem as a compact linear program. The latter paper also considers the polytope P D consisting of all matrices which are "near" to a given target matrix. We note that the ellipsoid algorithm in [3] also generalizes to the setting where one seeks a oblivious routing with minimum congestion for demand matrices belonging to a given polytope P D . This is essentially the separation problem for the robust network design with oblivious routing.. One well-studied special case of robust network design with oblivious routing is where traffic is assumed to obey the so-called hose model, introduced by Fingerhut et al. [10] and Duffield et al. [7] . In the symmetric marginals model, each node i specifies a marginal traffic amount b i (usually an integer), and a valid traffic matrix D is an assignment of unoriented demands D ij that respects the cumulative upper bounds {b i }: for each i, we have j D ij ≤ b i , where D ij = D ji represent the demand between i and j.. In the asymmetric marginals version of the hose model, each node i has two upper bounds, b. , which represent upper bounds on the amount of flow that the node i can send and receive, respectively. In other words, for a given bound vector b, the region P D , denoted by P(G, b), is defined as:. In the asymmetric marginal case, the network design problem is known to be coNP-hard in directed graphs [14] . The complexity of the problem in undirected graphs has not been established, even in the symmetric marginals case when all b i s are 1.. A related problem that has received particular attention is the so-called (asymmetric) virtual private network design problem (VPN problem). In this problem, the region P D is defined as in the asymmetric marginal case of the hose model. The routing is required to be oblivious, and furthermore it is restricted to use a single path for each pair of nodes. The asymmetric VPN problem is coNP-hard, even when we restrict to tree reservations [14] . Nevertheless, there are cases where finding an optimal tree reservation is easy, namely: (1) the asymmetric balanced case, i.e., when v∈T b [15] ; (2) the symmetric case [14] . Constant factor approximation algorithms for both the asymmetric and the symmetric VPN problems can be found in [8, [13] [14] [15] 19] , see [8] for a survey. In [1] a compact linear mixed-integer programming formulation for the asymmetric problem is given; it is also shown that this compact formulation allows to solve mediumto-large-size instances to optimality with commercial solvers, while a branch-and-price and cutting plane algorithm allows to tackle larger instances.. In [9] a cutting plane algorithm is devised to obtain empirical evidence that allowing fractional routing templates leads to significant cost reductions for the hose model. In [23] several robust design problems are considered; a "robustness premium" is measured and empirical evidence based on equipment costs is rendered. In [20] , an argument similar to one from [2] is used to obtain a compact LP formulation for maximizing throughput of oblivious routings for the class of hose demand matrices.. Confusion often occurs since instances may have oriented or unoriented demands, asymmetric or symmetric marginals, and flow vectors may be in directed or undirected graphs. It is worth keeping in mind that for directed graphs, or undirected graphs with asymmetric marginals, only oriented demands make sense. While our result is essentially about unoriented demands in undirected graphs, we found it simplest to present our proof in terms of oriented demands in a single-source flow problem in undirected graphs.

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


The variational iteration method: A highly promising method for solving the system of integro-differential equations This paper applies He's variational iteration method for solving two systems of Volterra integro-differential equations. The solution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exact solutions shows that the used method is an effective and highly promising method for various classes of both linear and nonlinear integro-differential equations. Integro-differential equations arise in many physical processes, such as glass-forming process [1], nanohydrodynamics [2], drop wise condensation [3] , and wind ripple in the desert [4] . There are various numerical and analytical methods to solve such problems, for example, the homotopy perturbation method [5] , the Adomian decomposition method [6] , but each method limits to a special class of integro-differential equations. Recently the variational iteration method [7] [8] [9] [10] has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations converging rapidly to accurate solutions [11] [12] [13] [14] [15] [16] [17] [18] . In Refs. [19] [20] [21] [22] the method was applied successfully to solve some integro-differential equations. Xu [20] first applied the variational iteration method to integral equations, Sweilam [21] applied the method to fourth-order integro-differential equations, and Wang et al. [19] found that the variational iteration method is an efficient algorithm for solving integro-differential equations by using some examples. The variational iteration method may be regarded with considerable justification as a versatile and promising method for solving all kinds of integro-differential equations.

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


Classification of Electromyographic Signals: Comparing Evolvable Hardware to Conventional Classifiers Abstract-Evolvable hardware (EHW) has shown itself to be a promising approach for prosthetic hand controllers. Besides competitive classification performance, EHW classifiers offer self-adaptation, fast training, and a compact implementation. However, EHW classifiers have not yet been sufficiently compared to state-of-the-art conventional classifiers. In this paper, we compare two EHW approaches to four conventional classification techniques: k-nearest-neighbor, decision trees, artificial neural networks, and support vector machines. We provide all classifiers with features extracted from electromyographic signals taken from forearm muscle contractions, and let the algorithms recognize eight to eleven different kinds of hand movements. We investigate classification accuracy on a fixed data set and stability of classification error rates when new data is introduced. For this purpose, we have recorded a short-term data set from three individuals over three consecutive days and a long-term data set from a single individual over three weeks. Experimental results demonstrate that EHW approaches are indeed able to compete with state-of-the-art classifiers in terms of classification performance.Index Terms-Classification of electromyographic signals, embedded Cartesian genetic programming, evolvable hardware, functional unit row architecture, prosthetic hand control. The first known prosthesis controlled by electromyography signals is the "Hüfner Hand" [13] . In 1948, Reiter implemented a prosthesis controller using one EMG channel to encode "open" and "close" movements of an artificial hand [14] . A quick contraction and relaxation triggered the "open" movement and a steady force contraction caused the prosthesis to gradually close the hand. Driven by the availability of compact electronic components, the area of prosthesis control gained more popularity in the 1960s and 1970s. Substantial effort went into defining strategies for robust selection of prosthesis actions from muscular activities [15] [16] [17] [18] [19] . The first commercial system was offered in the early 1960s [20] . In the following, we discuss modern EMG signal classification techniques with both conventional systems and EHW.

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


Enhancing 3D mesh topological skeletons with discrete contour constrictions Abstract This paper describes a unified and fully automatic algorithm for Reeb graph construction and simplification as well as constriction approximation on triangulated surfaces. The key idea of the algorithm is that discrete contours -curves carried by the edges of the mesh and approximating the continuous contours of a mapping function -encode both topological and geometrical shape characteristics. Therefore, a new concise shape representation, enhanced topological skeletons, is proposed, encoding the contours' topological and geometrical evolution. First, mesh feature points are computed. Then they are used as geodesic origins for the computation of an invariant mapping function that reveals the shape most significant features. Next, for each vertex in the mesh, its discrete contour is computed. As the set of discrete contours recovers the whole surface, each of them can be analyzed, both to detect topological changes and constrictions. Constriction approximations enable Reeb graphs refinement into more visually meaningful skeletons, which we refer to as enhanced topological skeletons. Extensive experiments showed that, without any preprocessing stage, proposed algorithms are fast in practice, affine-invariant and robust to a variety of surface degradations (surface noise, mesh sampling and model pose variations). These properties make enhanced topological skeletons interesting shape abstractions for many computer graphics applications. Polygonal mesh is a widely used representation of 3D shapes, mainly for exchange and display purposes. However, many applications in computer graphics need higher level shape descriptions as input. Topological skeletons have shown to be interesting shape descriptions [4] . They are beneficial for diverse fields like shape metamorphosis [25] , deformation [8] , retrieval [16] , texture mapping [35] , and so on.. Many topological approaches study the properties of real valued functions computed over triangulated surfaces.. Most of the time, those functions are provided by the application context, such as scientific data analysis [7] . When dealing with topological skeletons, it is necessary to define an invariant and visually interesting mapping function, which remains an open issue [4] .. Moreover, traditional topological graph construction algorithms assume that all the information brought by the mapping function is pertinent, while in practice, this can lead to large graphs [9, 24] , encoding noisy details.. Finally, topological approaches cannot discriminate visually interesting subparts of identified connected compo-nents, like the phalanxes of a finger. This is detrimental to certain applications, such as mesh deformation.. In this paper, an original and unified framework is proposed to address the above issues. Given a closed connected triangulated surface T , feature points are firstly extracted (Fig. 1a) in order to compute an invariant mapping function, noted f m (Fig. 1b) , which reveals the shape most significant parts. Secondly, for each vertex in the mesh, we compute its discrete contour, a connected curve traversing it and approximating f m continuous contours. We show that a topological analysis of those discrete contours enables a pertinent Reeb graph construction and simplification (Fig. 1c) , without any input parameter. Finally, we show that a geometrical analysis of discrete contours can approximate constrictions on prominent components (Fig. 1d) , enabling the refinement of Reeb graphs into enhanced topological skeletons (Fig. 1e) .. This paper, which extends the authors' previous work [32] , is structured as follows. First, we introduce topological skeleton related work. Next, we define our mapping function f m . Then, we present our algorithm for discrete contour computation, which is used both for the Reeb graph construction and simplification as well as the constriction approximation.. In particular, special emphasis is given to the discrete contour constriction detection algorithm, which provides more robust and more accurate results than the previous work [32] . Moreover, an extensive discussion on experimental results and framework evaluation is pro- Fig. 1a -g. Main steps of the framework. First, feature points are extracted (a). Then a mapping function (b) is contoured both to construct a topological skeleton (c) and to enhance it (e) with constrictions (d). Topology driven segmentation (f) and skeleton driven deformation (g) are two examples of application of the framework posed. Finally, to demonstrate the usability of the presented method, two applications are discussed: topology driven mesh segmentation (Fig. 1f) and skeleton driven mesh deformation (Fig. 1g ). In this paper, we presented a new concise shape abstraction, enhanced topological skeleton, that encodes both topological and geometrical evolutions of some mapping function contours. We also proposed a unified and fully automatic algorithm for its extraction. First, it computes a Reeb graph. Then it refines it by using discrete contour constriction as boundaries. To the authors' knowledge, this is the first approach that unifies Reeb graph construction and constriction computations.. Three scientific contributions are given. First, we proposed a robust and straightforward algorithm for feature point extraction. It enables the computation of an invariant mapping function which reveals well the shape most significant features. Secondly, we presented an algorithm for discrete contour computation. We showed that a topological analysis of these discrete contours enables a unified Reeb graph construction and simplification process. Finally, we showed that a geometrical analysis of the discrete contours provides visual perception conforming constriction approximations, enabling the refinement of the traditional Reeb graphs into more visually meaningful skeletons.. Moreover, we presented an extensive evaluation discussion of experimental results, according to four criteria. First, we have shown that enhanced topological skeletons respect shape skeleton intrinsic descriptive properties [33] , improving traditional topological skeletons description quality. Second, we have shown that the presented algorithm runs significantly faster than state-ofthe-art methods. Third, we have shown that enhanced topological skeletons are affine-invariant and robust to a variety of surface degradations, such as surface noise, mesh sampling variation and surface deformation. And finally, to evaluate the usability of the presented framework, we developed two applications related to topology driven mesh segmentation and skeleton driven mesh deformation.. Some limitations have been enumerated in the discussion. In future work, we would like to capture the notion of perceived symmetry in order to extract symmetrical skeletons if the objects seem roughly symmetrical. We believe this could benefit many applications, like surface similarity estimation. As a long term perspective, we would like to use enhanced topological skeletons as a shape abstraction for mesh editing operations within the framework of modeling by example systems [12] . Intermediary results and topological skeletons are shown in Figs. 14 and 15. On these illustrations, the reader can notice that enhanced topological skeletons concisely en-code both shape topology (Reeb graph, in blue) and geometry (constrictions, in red). On the one hand, the topological analysis results in the identification of the most significant topological components only, preserving the topological properties of the shape: model in Fig. 15e is a 1-genus surface and its skeleton consequently contains a cycle. On the other hand, the geometrical analysis enables the subdivision of these topological components into more visually meaningful subparts, increasing the description quality of traditional topological skeletons (subdividing humanoid models' limbs along potential articulations). According to Wu et al. [33] , a shape skeleton is expected to respect certain intrinsic properties: simplicity, stability, meaningfulness, neutrality and hierarchy. Firstly, as illustrated in Fig. 13a , enhanced topological skeletons can be collapsed into very concise representations. Secondly, the stability of the presented method can be observed in Fig. 15f and Fig. 15g , where two different horse models have nearly identical skeletons. More generally, the overall robustness of the framework will be addressed later in this discussion. Thirdly, the reader can see that no noisy details are encoded in the skeletons, which shows the meaningfulness of the framework. Fourthly, the neutrality of the skeleton is provided by the medial axis embedding we proposed in Sect. 9. Fifthly, a natural skeleton hierarchy is provided by the mapping function f m : skeleton subparts at the center of the object, at the root of the hierarchy, have a low function value (denoted in dark blue in Figs. 14 and 15) whereas extremity parts have a high function value (denoted in light blue in Figs. 14 and 15). Consequently, we can state that enhanced topological skeletons respect the intrinsic properties of shape skeletons [33] , and consequently provides a good description of 3D meshes. Feature points have been extracted in the past. Contrary to the algorithm presented by Mortara et al. [23] , the presented method resolves extraction on constant curvature areas, such as a sphere where two poles are extracted (Fig. 14a) . Moreover, the algorithm presented by Katz et al. [17] runs in quadratic execution complexity while our algorithm needs O(n × log(n)) steps, with n the number of vertices in the mesh. At last, we can state that our feature point extraction algorithm leads to visual perception conforming results, as shown in Fig. 16b , c where feature points have been extracted on the extremity of each finger and toe.. As for the topological skeleton construction algorithm, the reader can notice that no noisy details have been encoded in the skeletons, because discrete contours do not disconnect in f m non-smooth configurations (denoted with red and black critical points in Fig. 6 ). Contrary to traditional Reeb graph simplification algorithms, no noisecorrective threshold is required.. Discrete contour constriction detection also leads to visual perception conforming results, identifying the most significant surface bottlenecks (such as the humanoid models' elbows and knees for example). As shown in Fig. 14n , o the proposed algorithms leads to acceptable results even with coarsely designed objects, even on strongly tubular components. Notice that it also behaves correctly with primitive shapes, such as the sphere (Fig. 14m) , where no constriction is identified. Moreover, contrary to previous works [14, 15] , only meaningful constrictions are extracted. Several approaches have been explored for the decomposition of polygonal meshes into meaningful subcomponents, to extract skeletal representations of shapes. They can be roughly classified into four categories: semanticoriented segmentations, medial axis transforms, generalized potential fields and topological skeletons. Each one has its own advantages and drawbacks. For example, medial axis transform based methods [6, 26] are commonly associated with the drawback of high sensitiveness to small surface perturbations, which is detrimental to many applications. On the contrary, generalized potential field based methods [33] provide more robust results at the cost of high computational times. In comparison to mesh segmentation based methods [2, 17, 18] and traditional skeleton extraction [33] , topological approaches, based on Morse and Reeb graph theories [22, 28] , present the advantage of preserving the topological properties of the shape [4] (number of loops, number and relations between components, etc.). However, with regard to shape skeletons, we identify three main drawbacks in topological approaches, successively addressed in this paper.. Firstly, it is difficult to define an invariant and visually interesting mapping function. Secondly, constructing and transforming a topological graph into a manageable skeleton is not a trivial problem. Finally, topological approaches decompose a surface into connected subcomponents only. This means that visually interesting subparts of identified connected components will not be discriminated: for example, a finger of a hand model will not be decomposed into phalanxes.

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


Drug target identification in sphingolipid metabolism by computational systems biology tools: Metabolic control analysis and metabolic pathway analysis Sphingolipids regulate cellular processes that are critically important in cell's fate and function in cancer development and progression. This fact underlies the basics of the novel cancer therapy approach. The pharmacological manipulation of the sphingolipid metabolism in cancer therapeutics necessitates the detailed understanding of the pathway. Two computational systems biology tools are used to identify potential drug target enzymes among sphingolipid pathway that can be further utilized in drug design studies for cancer therapy. The enzymes in sphingolipid pathway were ranked according to their roles in controlling the metabolic network by metabolic control analysis. The physiologically connected reactions, i.e. biologically significant and functional modules of network, were identified by metabolic pathway analysis. The final set of candidate drug target enzymes are selected such that their manipulation leads to ceramide accumulation and long chain base phosphates depletion. The mathematical tools' efficiency for drug target identification performed in this study is validated by clinically available drugs. Sphingolipids comprise a class of complex lipids which are abundantly found in cell membrane. These membrane lipids do not only function as structural components of the cell membrane but they possess important roles in signal transduction (as second messengers) and in regulatory pathways such as cell cycle arrest, apoptosis, senescence and differentiation. The investigation of the processes that are regulated by bioactive sphingolipid signaling molecules demonstrates that sphingolipids are fundamental to cancer pathogenesis and therapeutics [1] . Ceramide, an essential building block of sphingolipids, has been suggested to be a reasonable key metabolite in cancer therapy inducing antiproliferative and apoptotic responses. Many anti-cancer drugs are reported to lead to increased endogenous ceramide levels. Ceramide's influence on cell growth is dynamically balanced by sphingosine-1-phosphate and this balance is termed as ''sphingolipid rheostat". In cancer cells, this dynamic balance is missing [1] [2] [3] [4] [5] [6] [7] [8] .. A novel cancer therapy approach resides on the adjustment of the sphingolipid metabolism to accumulate ceramide and to decrease sphingosine-1-phosphate based on the fact of ceramide being a ''tumor-suppressor lipid" and sphingosine-1-phosphate being a ''tumor-promoting lipid". The drugs using this fact are expected to resemble the antiproliferative and apoptotic responses in the cell by altering the sphingolipid levels. The advantages of such changes are not only in cancer therapy but also, enhancement of drug action and chemoprevention [1, [6] [7] [8] .. There are several newly developed synthetic inhibitors of specific enzymes involved in sphingolipid metabolism [9] . The target enzymes of human sphingolipid pathway are serine palmitoyl transferase, ceramide synthase, ceramidase, sphingosine kinase, glucosylceramide synthase, 1-O-acylceramide synthase. A number of drugs like N-4-hydroxyphenyl retinamide (4-HPR), Valspodar (PSC 833), daunorubicin, ceramide analog (B13), safingol, butyldeoxynojirimycin and phenoxodiol targeting the above listed enzymes are in pre-clinical or clinical development [7, [9] [10] [11] [12] . Changing ceramide levels in favor of cancer therapy seems to be a promising strategy if the developed drugs targeting the newly identified sphingolipid enzymes are selective toward malignant cells but not healthy cells. With some ceramidase inhibitor trials this selectivity seems to be possible due to the hypersensitivity of malignant cells to ceramide perturbation [7] . Another evidence for the significance of accumulation of ceramide in cancer cells is that cancer cells escape from apoptosis by degrading, catabolizing or converting ceramide [9] . Experimentalists observed elevated levels of acid ceramidase expression in human prostate cancer cell lines [13] . The manipulation of these cellular processes gives the chance of developing new anti-cancer therapeutics and indeed, forms the basics of the novel cancer therapy method [1] .. The most difficult step in drug discovery is the decision of the drug target enzymes. Since clinical aspects of sphingolipids are still lacking information, the identification of drug targets by employing computational tools is a significant requirement. Metabolic control analysis is a powerful mathematical tool to solve this puzzle of drug target identification via considering the role of individual components within a metabolic network [14] . As mentioned previously, sphingolipids regulate processes that are vital in terms of cell's fate. These processes are all very important for cancer initiation, progression and treatment [6] . The identification of critical enzymes within sphingolipid metabolism facilitates the link between sphingolipids and cancer.. In the present study, the key points of sphingolipid metabolism in terms of ceramide and sphingosine-1-phosphate are investigated using two different mathematical frameworks, metabolic control analysis and metabolic pathway analysis. Metabolic control analysis is based on dynamic data whereas metabolic pathway analysis uses the stoichiometry of the system. These two systems biology tools reveal the important metabolic steps of the sphingolipid pathway and using this information novel drug target enzymes can be recognized and potential drug target enzymes in human pathway can be proposed. Although the Saccharomyces cerevisiae and human sphingolipid pathways are similar to each other, one should admit that S. cerevisiae sphingolipid pathway consists of only few complex sphingolipids when compared with that of mammalian cells/human. Thus, this study can be considered as an attempt to bridge the basic sphingolipid research to potential medical applications in cancer therapy. When the two systems biology tools employed in the current study are compared in terms of their potency in potential drug target identification, it can be seen that metabolic pathway analysis results overlap more with the known drug targets in the literature. Metabolic control analysis results, on the other hand, are more informative since one can gather information about the direction of action, i.e. whether one should inhibit or activate the target enzyme. Thus, MCA results go one step further on the way to drug discovery and drug design.. In conclusion, the enzymes catalyzing the reactions 1, 2, 4, 5, 6, 9, 11, 12, 15, 20, 21, 23, 27 and 34 are proposed as putative drug targets by both MCA and MPA. The activities of palmitoylcoenzyme A synthase (r 1 ), glycerol-3-phosphate acyltransferase (r 2 ), CDP-DAG synthase (r 4 ), phosphatidylinositol synthase (r 5 ), 4-hydroxylase (r 21 ), ceramide synthase (r 23 ) and acetyl-coenzyme A synthetase (r 34 ) should be increased to obtain the ceramide accumulation and long chain base phosphate depletion and the activities of inositol-1-phosphate synthase (r 6 ), phosphoserinephosphatase (r 9 ), serine palmitoyl transferase (r 11 ), acyl-coenyzme A binding protein (r 12 ), sphingolipid long chain base kinase (r 15 and r 20 ) and GPI remodelase (r 27 ) should be decreased in order to reach the same cancer therapy essentials. Integration of the results of the two theoretical frameworks as we have done in this study can be utilized in future in other drug target identification studies.. In order to obtain more efficient drugs in cancer therapy; drugs targeting two or more enzymes may be developed or two or more drugs may be utilized at the same time course. There is clinical evidence of using drugs [7, 9] both inhibiting ceramide catabolism and generating ceramide simultaneously. We combined the results of the two mathematical tools (MCA and MPA) to obtain a more complete view and reached an ultimate set of potential drug target enzymes (Table 7) . These common enzymes that are indicated by both MCA and MPA results are of the reactions 1, 2, 9, 11 and 34 and they are identified by at least four out of five of the methods discussed here. Moreover, if the target enzymes that appear in at least one of the MCA selection algorithms and one of the MPA computations are also included in this final set, the enzymes catalyzing the reactions 4, 5 and 11 emerge to be the additional candidates. Besides these, the known drug target enzymes from the literature that are identified by the MPA results could also be included in the concluding set (r 11 , r 15 , r 20 , r 23 ). The target enzymes that are determined by all the three selection algorithms of MCA but not MPA, i.e. enzymes belonging to reactions 6 and 12, can be added to the candidate list due to their reliability by passing all selection criterions of MCA. Another reason for including reaction 6 in the ultimate set of potential drug targets is that the manipulation of the enzyme activity of reaction 6 does not disturb the complex sphingolipid concentrations much with the percent change values of À15.46%, 14.73% and À19.47% for the IPC, MIPC and M(IP) 2 C, respectively (Table 5 ). An ideal drug is expected not to affect the metabolism other than its targets.. Although not identified by MPA results, reactions 21 and 27 from MCA results are also taken into account due to reaction 27's essential effect on PHCer accumulation (37.95% change, Table 5 ) and reaction 21's almost null effect on complex sphingolipids. The manipulation of the enzyme activity of reaction 21 has its desired effects on ceramide accumulation and long chain base phosphate depletion but it does not change the complex sphingolipid content of the cell with respect to wild type, i.e. À22.42%, À18.56% and À8.85% alterations in IPC, MIPC and M(IP) 2 C's concentrations, respectively ( Table 5) .. The drug targets proposed in this study are found to be more conserved than the other enzymes in the sphingolipid network (Supplementary Table 1 ). Ceramide and sphingosine-1-phosphate, being the sphingolipid rheostat, are known to play critical roles in cell proliferation and cell's death. This fact about the two opposing signaling molecules leads us to investigate the effects of all ceramide related metabolites using metabolic control analysis and metabolic pathway analysis.

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