Methods of Regularities Searching Based on Optimal Partitioning

The purpose of discussed optimal valid partitioning (OVP) methods is uncovering of ordinal or continuous explanatory variables effect on outcome variables of different types. The OVP approach is based on searching partitions of explanatory variables space that in the best way separate observations with different levels of outcomes. Partitions of single variables ranges or two-dimensional admissible areas for pairs of variables are searched inside corresponding families. Statistical validity associated with revealed regularities is estimated with the help of permutation test repeating search of optimal partition for each permuted dataset. Method for output regularities selection is discussed that is based on validity evaluating with the help of two types of permutation tests.

Lateglacial and Holocene vegetation belts in the Pirin Mountains (southwestern Bulgaria)

Pollen stratigraphy of a core 270 cm long from Lake Dalgoto at 2310 m in the Northern Pirin Mountains, southern Bulgaria, was treated by optimal partitioning and compared to a broken-stick model to reveal statistically significant pollen zones. The vegetational reconstructions presented here are based on pollen percentages and pollen influx, on comparisons of modern and fossil pollen spectra, and on macrofossil dates from other sites in the mountains. During the Younger Dryas (11000–10200 14C yr BP), an open xerophytic herb vegetation with Artemisia and Chenopodiaceae was widely developed around the lake. Deciduous trees growing at lower elevations contributed to the pollen rain deposited at the higher-elevation sampling sites. Specifically, from 10200 to 8500 yr BP, Quercus, Ulmus, Tilia and Betula expanded rapidly at low and intermediate elevations, and between 8500 and 6500 yr BP they extended to higher elevations close to the upper forest limit, which was formed by Betula pendula at about 1900 m. Coniferous species were limited in the region at this time. After 6500 yr BP, the expansion of conifers (Pinus peuce, P. sylvestris, P. mugo, Abies alba) at high elevations forced the deciduous trees downward. Between 6500 and 3000 yr BP, the forest limit at 2200 m was formed by P. peuce, and A. alba had its maximum vertical range up to 1900 m. Later the abundance and vertical range of P. peuce and A. alba were reduced. After 3000 yr BP, Picea expanded.

On the k-anonymization of time-varying and multi-layer social graphs

The popularity of online social media platforms provides an unprecedented opportunity to study real-world complex networks of interactions. However, releasing this data to researchers and the public comes at the cost of potentially exposing private and sensitive user information. It has been shown that a naive anonymization of a network by removing the identity of the nodes is not sufficient to preserve users’ privacy. In order to deal with malicious attacks, k -anonymity solutions have been proposed to partially obfuscate topological information that can be used to infer nodes’ identity. In this paper, we study the problem of ensuring k anonymity in time-varying graphs, i.e., graphs with a structure that changes over time, and multi-layer graphs, i.e., graphs with multiple types of links. More specifically, we examine the case in which the attacker has access to the degree of the nodes. The goal is to generate a new graph where, given the degree of a node in each (temporal) layer of the graph, such a node remains indistinguishable from other k-1 nodes in the graph. In order to achieve this, we find the optimal partitioning of the graph nodes such that the cost of anonymizing the degree information within each group is minimum. We show that this reduces to a special case of a Generalized Assignment Problem, and we propose a simple yet effective algorithm to solve it. Finally, we introduce an iterated linear programming approach to enforce the realizability of the anonymized degree sequences. The efficacy of the method is assessed through an extensive set of experiments on synthetic and real-world graphs.

Dynamic Resource Allocation in Wireless Heterogeneous Networks

Deployment of low power basestations within cellular networks can potentially increase both capacity and coverage. However, such deployments require efficient resource allocation schemes for managing interference from the low power and macro basestations that are located within each other’s transmission range. In this dissertation, we propose novel and efficient dynamic resource allocation algorithms in the frequency, time and space domains. We show that the proposed algorithms perform better than the current state-of-art resource management algorithms. In the first part of the dissertation, we propose an interference management solution in the frequency domain. We introduce a distributed frequency allocation scheme that shares frequencies between macro and low power pico basestations, and guarantees a minimum average throughput to users. The scheme seeks to minimize the total number of frequencies needed to honor the minimum throughput requirements. We evaluate our scheme using detailed simulations and show that it performs on par with the centralized optimum allocation. Moreover, our proposed scheme outperforms a static frequency reuse scheme and the centralized optimal partitioning between the macro and picos. In the second part of the dissertation, we propose a time domain solution to the interference problem. We consider the problem of maximizing the alpha-fairness utility over heterogeneous wireless networks (HetNets) by jointly optimizing user association, wherein each user is associated to any one transmission point (TP) in the network, and activation fractions of all TPs. Activation fraction of a TP is the fraction of the frame duration for which it is active, and together these fractions influence the interference seen in the network. To address this joint optimization problem which we show is NP-hard, we propose an alternating optimization based approach wherein the activation fractions and the user association are optimized in an alternating manner. The subproblem of determining the optimal activation fractions is solved using a provably convergent auxiliary function method. On the other hand, the subproblem of determining the user association is solved via a simple combinatorial algorithm. Meaningful performance guarantees are derived in either case. Simulation results over a practical HetNet topology reveal the superior performance of the proposed algorithms and underscore the significant benefits of the joint optimization. In the final part of the dissertation, we propose a space domain solution to the interference problem. We consider the problem of maximizing system utility by optimizing over the set of user and TP pairs in each subframe, where each user can be served by multiple TPs. To address this optimization problem which is NP-hard, we propose a solution scheme based on difference of submodular function optimization approach. We evaluate our scheme using detailed simulations and show that it performs on par with a much more computationally demanding difference of convex function optimization scheme. Moreover, the proposed scheme performs within a reasonable percentage of the optimal solution. We further demonstrate the advantage of the proposed scheme by studying its performance with variation in different network topology parameters.

Partitioning of reproduction in mother-daughter versus sibling associations : a test of optimal skew theory

A critical feature of cooperative animal societies is the reproductive skew, a shorthand term for the degree to which a dominant individual monopolizes overall reproduction in the group. Our theoretical analysis of the evolutionarily stable skew in matrifilial (i.e., mother-daughter) societies, in which relatednesses to offspring are asymmetrical, predicts that reproductive skews in such societies should tend to be greater than those of semisocial societies (i.e., societies composed of individuals of the same generation, such as siblings), in which relatednesses to offspring are symmetrical. Quantitative data on reproductive skews in semisocial and matrifilial associations within the same species for 17 eusocial Hymenoptera support this prediction. Likewise, a survey of reproductive partitioning within 20 vertebrate societies demonstrates that complete reproductive monopoly is more likely to occur in matrifilial than in semisocial societies, also as predicted by the optimal skew model.

Data partitioning for parallel spatial join processing

The cost of spatial join processing can be very high because of the large sizes of spatial objects and the computation-intensive spatial operations. While parallel processing seems a natural solution to this problem, it is not clear how spatial data can be partitioned for this purpose. Various spatial data partitioning methods are examined in this paper. A framework combining the data-partitioning techniques used by most parallel join algorithms in relational databases and the filter-and-refine strategy for spatial operation processing is proposed for parallel spatial join processing. Object duplication caused by multi-assignment in spatial data partitioning can result in extra CPU cost as well as extra communication cost. We find that the key to overcome this problem is to preserve spatial locality in task decomposition. We show in this paper that a near-optimal speedup can be achieved for parallel spatial join processing using our new algorithms.

Task partitioning and priority assignment for distributed hard real-time systems

In this paper, we propose the Distributed using Optimal Priority Assignment (DOPA) heuristic that finds a feasible partitioning and priority assignment for distributed applications based on the linear transactional model. DOPA partitions the tasks and messages in the distributed system, and makes use of the Optimal Priority Assignment (OPA) algorithm known as Audsley’s algorithm, to find the priorities for that partition. The experimental results show how the use of the OPA algorithm increases in average the number of schedulable tasks and messages in a distributed system when compared to the use of Deadline Monotonic (DM) usually favoured in other works. Afterwards, we extend these results to the assignment of Parallel/Distributed applications and present a second heuristic named Parallel-DOPA (P-DOPA). In that case, we show how the partitioning process can be simplified by using the Distributed Stretch Transformation (DST), a parallel transaction transformation algorithm introduced in [1].

An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

In this work, we deal with the problem of packing (orthogonally and without overlapping) identical rectangles in a rectangle. This problem appears in different logistics settings, such as the loading of boxes on pallets, the arrangements of pallets in trucks and the stowing of cargo in ships. We present a recursive partitioning approach combining improved versions of a recursive five-block heuristic and an L-approach for packing rectangles into larger rectangles and L-shaped pieces. The combined approach is able to rapidly find the optimal solutions of all instances of the pallet loading problem sets Cover I and II (more than 50 000 instances). It is also effective for solving the instances of problem set Cover III (almost 100 000 instances) and practical examples of a woodpulp stowage problem, if compared to other methods from the literature. Some theoretical results are also discussed and, based on them, efficient computer implementations are introduced. The computer implementation and the data sets are available for benchmarking purposes. Journal of the Operational Research Society (2010) 61, 306-320. doi: 10.1057/jors.2008.141 Published online 4 February 2009

Use Multilevel Graph Partitioning Scheme to solve traveling salesman problem

The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.

5CN05 partitioning in an aqueous two-phase system: A new approach to the solubilization of hydrophobic drugs

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Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method. Journal of the Operational Research Society (2012) 63, 183-200. doi: 10.1057/jors.2011.6 Published online 17 August 2011

Clutch-size adjustments and skew models: effects on reproductive partitioning and group stability

Reproductive skew theory seeks to integrate social and ecological factors thought to influence the division of reproduction among group-living animals. However, most reproductive skew models only examine interactions between individuals of the same sex. Here, we suggest that females can influence group stability and conflict among males by modifying their clutch size and may do so if they benefit from the presence of subordinate male helpers or from reduced conflict. We develop 3 models, based on concessions-based, restraint, and tug-of-war models, in which female clutch size is variable and ask when females will increase their clutch size above that which would be optimal in the absence of male-male conflict. In concessions-based and restraint models, females should increase clutch size above their optima if the benefits of staying for subordinate males are relatively low. Relatedness between males has no effect on clutch size. When females do increase clutch size, the division of reproduction between males is not influenced by relatedness and does not differ between restraint and concessions-based models. Both of these predictions are in sharp contrast to previous models. In tug-of-war models, clutch size is strongly influenced by relatedness between males, with the largest clutches, but the fewest surviving offspring, produced when males are unrelated. These 3 models demonstrate the importance of considering third-party interests in the decisions of group-living organisms.

Postseptational chromosome partitioning in bacteria.

Mutations in the spoIIIE gene prevent proper partitioning of one chromosome into the developing prespore during sporulation but have no overt effect on partitioning in vegetatively dividing cells. However, the expression of spoIIIE in vegetative cells and the occurrence of genes closely related to spoIIIE in a range of nonsporulating eubacteria suggested a more general function for the protein. Here we show that SpoIIIE protein is needed for optimal chromosome partitioning in vegetative cells of Bacillus subtilis when the normal tight coordination between septation and nucleoid partitioning is perturbed or when septum positioning is altered. A functional SpoIIIE protein allows cells to recover from a state in which their chromosome has been trapped by a closing septum. By analogy to its function during sporulation, we suggest that SpoIIIE facilitates partitioning by actively translocating the chromosome out of the septum. In addition to enhancing the fidelity of nucleoid partitioning, SpoIIIE also seems to be required for maximal resistance to antibiotics that interfere with DNA metabolism. The results have important implications for our understanding of the functions of genes involved in the primary partitioning machinery in bacteria and of how septum placement is controlled.

Identifying optimal lipid raft characteristics required to promote nanoscale protein-protein interactions on the plasma membrane

The dynamic lateral segregation of signaling proteins into microdomains is proposed to facilitate signal transduction, but the constraints on microdomain size, mobility, and diffusion that might realize this function are undefined. Here we interrogate a stochastic spatial model of the plasma membrane to determine how microdomains affect protein dynamics. Taking lipid rafts as representative microdomains, we show that reduced protein mobility in rafts segregates dynamically partitioning proteins, but the equilibrium concentration is largely independent of raft size and mobility. Rafts weakly impede small-scale protein diffusion but more strongly impede long-range protein mobility. The long-range mobility of raft-partitioning and raft-excluded proteins, however, is reduced to a similar extent. Dynamic partitioning into rafts increases specific interprotein collision rates, but to maximize this critical, biologically relevant function, rafts must be small (diameter, 6 to 14 nm) and mobile. Intermolecular collisions can also be favored by the selective capture and exclusion of proteins by rafts, although this mechanism is generally less efficient than simple dynamic partitioning. Generalizing these results, we conclude that microdomains can readily operate as protein concentrators or isolators but there appear to be significant constraints on size and mobility if microdomains are also required to function as reaction chambers that facilitate nanoscale protein-protein interactions. These results may have significant implications for the many signaling cascades that are scaffolded or assembled in plasma membrane microdomains.

Robust H.264/AVC video transmission using data partitioning and unequal loss protection

In this work, we present an adaptive unequal loss protection (ULP) scheme for H264/AVC video transmission over lossy networks. This scheme combines erasure coding, H.264/AVC error resilience techniques and importance measures in video coding. The unequal importance of the video packets is identified in the group of pictures (GOP) and the H.264/AVC data partitioning levels. The presented method can adaptively assign unequal amount of forward error correction (FEC) parity across the video packets according to the network conditions, such as the available network bandwidth, packet loss rate and average packet burst loss length. A near optimal algorithm is developed to deal with the FEC assignment for optimization. The simulation results show that our scheme can effectively utilize network resources such as bandwidth, while improving the quality of the video transmission. In addition, the proposed ULP strategy ensures graceful degradation of the received video quality as the packet loss rate increases. © 2010 IEEE.