Partition Of Universe Research Articles

Impact of gate-level clustering on automated system partitioning of 3D-ICs

When partitioning gate-level netlists using graphs, it is beneficial to cluster gates to reduce the order of the graph and preserve some characteristics of the circuit that the partitioning might degrade. Gate clustering is even more important for netlist partitioning targeting 3D system integration. In this paper, we make the argument that the choice of clustering method for 3D-ICs partitioning is not trivial and deserves careful consideration. To support our claim, we implemented three clustering methods that were used prior to partitioning two synthetic designs representing two extremes of the circuits medium/long interconnect diversity spectrum. Automatically partitioned netlists are then placed and routed in 3D to compare the impact of clustering methods on several metrics. From our experiments, we see that the clustering method indeed has a different impact depending on the design considered and that a circuit-blind, universal partitioning method is not the way to go, with wire-length savings of up to 31%, total power of up to 22%, and effective frequency of up to 15% compared to other methods. Furthermore, we highlight that 3D-ICs open new opportunities to design systems with a denser interconnect, drastically reducing the design utilization of circuits that would not be considered viable in 2D.

On the origin of the combinatorial complexity of the crystal structures with 0D, 1D, or 2D primary motifs

Based on Krivovichev information measures for crystal structures and the universal partitioning scheme for different sources of information described previously by Hornfeck, we proposed a general scheme of complexity calculation for heterodesmic crystals.

High-Throughput Bin Packing: Scheduling Jobs With Random Resource Demands in Clusters

We consider a natural scheduling problem which arises in many distributed computing frameworks. Jobs with diverse resource demands (e.g. memory requirements) arrive over time and must be served by a cluster of servers. To improve throughput and delay, the scheduler can pack as many jobs as possible in each server, however the sum of the jobs' resource demands cannot exceed the server's capacity. Motivated by the increasing complexity of workloads in shared clusters, we consider a setting where jobs' resource demands belong to a very large set of diverse types, or in the extreme case even infinitely many types, i.e. resource demands are drawn from a general unknown distribution over a possibly continuous support. The application of classical scheduling approaches that crucially rely on a predefined finite set of types is discouraging in this high (or infinite) type setting. We first characterize a fundamental limit on the maximum throughput in such setting. We then develop oblivious scheduling algorithms, based on Best-Fit and Universal Partitioning, that have low complexity and can achieve at least 1/2 and 2/3 of the maximum throughput respectively, without the knowledge of the resource demand distribution. Extensive simulation results, using both synthetic and real traffic traces, are presented to verify the performance of our algorithms.

A universal partition result for infinite homogeneous [formula omitted]-free and related graphs

We study new partition properties of infinite Kn-free graphs. First, we investigate the number bpi(G,m) introduced by A. Aranda et al. (denoted there by r(G,m)) : the minimal r so that for any partition of G into r classes of equal size, there exists an independent set which meets at least m classes in size |G|. In the case of Henson’s countable universal Kn-free graph Hn, we express bpi(Hnm) by well-known Ramsey-numbers for finite digraphs. In particular we answer a conjecture of Thomassé (2000) by showing that indeed bpi(Hn,2)=2 for all n⩾3. Furthermore, we bound and in some cases determine bpi(G,m) for certain geometric graphs, including shift graphs, unit distance graphs and orthogonality graphs.Second, we prove a new universal partition property for Hn. Given a finite bipartite graph G on classes A,B, we show that for any balanced 2-colouring of Hn there is an induced copy of G in Hn so that the images of A and B are monochromatic of distinct colours. We end our paper with further open problems.

A Data-Driven Approach Using 911-Call Data to Reconfigure Police Beat Zones

Finding the optimal boundaries of police beat zones is a challenging task due to the dynamic nature of 911-calls that vary over space and time. The lack of a data-driven approach for delineating these boundaries produces non-uniform demand across beat zones, thus resulting in an uneven distribution of workload among officers. We analyzed 911-calls received in a mid-sized Texas city over a period of 4 years and found differences in service call volume serviced by each of the five current beat zones that lead to workload disparities and uneven response times. Readily available 911-service call data integrated into Geographic Information Systems can be used to create boundaries of police beat zones that aim to minimize the differences in the number of service calls originating from each beat zone. Most recently developed approach, the Universal PArtitioning System, was used to produce contiguous spatial partitions of approximately equal call volume resulting in configurations that have a more uniform distribution of calls thus reducing the disparities in officer workload between beat zones. The efficiency of using a computational, data-driven approach allows police to evaluate the impacts of several beat zone configurations on their ability to provide service with respect to available resources.

Partition function of Chern–Simons theory as renormalized q-dimension

We calculate $q$-dimension of $k$-th Cartan power of fundamental representation $\Lambda_0$, corresponding to affine root of affine simply laced Kac-Moody algebras, and show that in the limit $q\rightarrow 1 $, and with natural renormalization, it is equal to universal partition function of Chern-Simons theory on three-dimensional sphere.

Universal volume of groups and anomaly of Vogel’s symmetry

We show that integral representation of universal volume function of compact simple Lie groups gives rise to six analytic functions on $CP^2$, which transform as two triplets under group of permutations of Vogel's projective parameters. This substitutes expected invariance under permutations of universal parameters by more complicated covariance. We provide an analytical continuation of these functions and particularly calculate their change under permutations of parameters. This last relation is universal generalization, for an arbitrary simple Lie group and an arbitrary point in Vogel's plane, of the Kinkelin's reflection relation on Barnes' $G(1+N)$ function. Kinkelin's relation gives asymmetry of the $G(1+N)$ function (which is essentially the volume function for $SU(N)$ groups) under $N\leftrightarrow -N$ transformation (which is equivalent of the permutation of parameters, for $SU(N)$ groups), and coincides with universal relation on permutations at the $SU(N)$ line on Vogel's plane. These results are also applicable to universal partition function of Chern-Simons theory on three-dimensional sphere. This effect is analogous to modular covariance, instead of invariance, of partition functions of appropriate gauge theories under modular transformation of couplings.

On a Gopakumar-Vafa form of partition function of Chern-Simons theory on classical and exceptional lines

We show that partition function of Chern-Simons theory on three-sphere with classical and exceptional groups (actually on the whole corresponding lines in Vogel's plane) can be represented as ratio of respectively triple and double sine functions (last function is essentially a modular quantum dilogarithm). The product representation of sine functions gives Gopakumar-Vafa structure form of partition function, which in turn gives a corresponding integer invariants of manifold after geometrical transition. In this way we suggest to extend gauge/string duality to exceptional groups, although one still have to resolve few problems. In both classical and exceptional cases an additional terms, non-perturbative w.r.t. the string coupling constant, appear. The full universal partition function of Chern-Simons theory on three-sphere is shown to be the ratio of quadruple sine functions. We also briefly discuss the matrix model for exceptional line.

The Mathematical Abstraction Theory, The Fundamentals for Knowledge Representation and Self-Evolving Autonomous Problem Solving Systems

The study represents a new way to describe knowledge with generalized universal algebra allowing loop structures so very important in AI languages and which gives an extensive variety of notional relations between net entities without restricting the semantic use. Consequently a new syntax model for solving problems defined by said nets is established flexibly utilizing notional similarities with original problems to further match solutions in memory data banks thus additionally creating transducer graphs of solving rewrite systems and thereof closure system of solving classes. The study introduces universal partitioning to widen environmental attachments subject to abstraction relations, yielding universal macros from parallel TD-solutions. Net NUO-presentations are delivered providing more general coverage enabling net block homomorphism to be used for TD-solution generation. A special attention is given to cardinalities of basic solutions. Second order parallel relation is introduced for distinct solution set bases. Finally direct products of power sets in abstraction relations serve as ingredients for multiple level abstraction algebra which is taken in account for determining self-evolving solving systems. This is reached by tree different stages offering combinational approach in multiple power solution families and iterative solving, thus creating solution basis for evolutional levels.

An enhanced fuzzy time series forecasting method based on artificial bee colony

In recent years, several forecasting methods have been proposed for the analysis of fuzzy time series. Determination of fuzzy relations and establishing interval lengths, which is used in partition of universe of discourse, can be considered as the two of main elements affecting the forecasting performance of these forecasting methods. In the literature, along with the studies in which interval lengths are determined subjectively, algorithms such as genetic algorithms and particle swarm optimization have been utilized. In this study, a new fuzzy time series forecasting method which uses Artificial Bee Colony (ABC) algorithm for the determination of interval lengths for the first time in the literature is proposed. To obtain forecasts, this new method makes use of fuzzy logic relationship tables in determining the fuzzy relations and also uses estimating based on next state (EBN) for training set and master voting (MV) scheme for test set. The new proposed method is applied to three various time series and when compared with the existing methods better results are obtained with regard to both training and test set..

Universal Chern-Simons partition functions as quadruple Barnes’ gamma-functions

We show that both perturbative and non-perturbative parts of universal partition functions of Chern-Simons theory on 3d sphere are ratios of four over four Barnes' quadruple gamma functions with arguments given by linear combinations of universal parameters. Since nonperturbative part of partition function is essentially a universal compact simple Lie group's volume, latter appears to be expressed through quadruple Barnes' functions, also. For SU(N) values of parameters recurrent relations on Barnes' functions give the proof of level-rank duality of complete partition function, thus extending that duality on non-integer level and rank. We note that integral representation of universal partition function is defined on few disjoint regions in parameters' space, corresponding to different signs of real parts of parameters, and introduce a framework for discussion of analytic continuation of partition functions(s) from these regions. Although initial integral representation is symmetric under all permutations of parameters (which corresponds particularly to $N \rightarrow -N$ duality of gauge theories with classical groups), analytic continuations are not symmetric under transposition of parameters with different signs of their real parts. For the particular case of SU(N) Chern-Simons this asymmetry appears to be the Kinkelin's functional equation (reflection relation) for Barnes' G-function.

Quick Attribute Reduction Based on Approximation Dependency Degree

Attribute reduction is one of the core research content of Rough sets theory. Many existing algorithms mainly are aimed at the reduction of consistency decision table, and very little work has been done for attribute reduction aimed at inconsistency decision table. In fact, the methods finding Pawlak reduct from consistent decision table are not suitable for inconsistency decision table. In this paper, we introduce the approximation dependency reduction modal and present the Quick Attribution Reduction based on Approximation Dependency Degree (Quick-ARADD), which can retain the original boundary region and the original positive region unchanged, and keep the approximation accuracy unchanged for all decision equivalence classes (the partition of universe on decision attributes) of a decision table. Theoretical analysis and experimental results show that the Quick-ARADD algorithm is effective and feasible.

Integration of fuzzy logic with response surface methodology for thrust force and surface roughness modeling of drilling on titanium alloy

In recent years, a lot of extensive research work has been carried out in drilling operations for achieving better hole quality. Drilling operation is one of the machining processes, and it widely used in aeronautical and automotive industries for assembling the parts. The surface roughness is one of the significant factors in drilling operation because the poor surface finish will affect the material condition during the assembly. The spindle speed and feed rate are the important factors to affect the surface finish. In addition, the detailed analysis of the thrust force is also to be investigated for characterizing the cutting process. However, for examining the machining characteristics more trial runs are required, and it increases the time and cost of the experiment. In this paper, the integration of fuzzy logic (FL) with response surface methodology (RSM) has been introduced to reduce the cost and the time consumption for investigation. The low, middle, and upper levels of spindle speed with low and upper levels of feed rate combinations were examined on cutting force and surface finish through the experimental setup with the systematic manner. The FL model for thrust force and surface finish were obtained from the collected experimental data. The FL model has developed another two combinations of data without experimentation through universal partitioning. The results show that the predicted FL values are within the range of experimental value. Therefore, the FL model values were selected for further investigation with RSM. The result of FL-RSM model values are also within the range of experimental value. The proposed FL-RSM model and FL model are validated with experimental results. Finally, the validated results show that hybrid FL-RSM produces the effective output than the FL model.

Rule learning for classification based on neighborhood covering reduction

Rough set theory has been extensively discussed in the domain of machine learning and data mining. Pawlak’s rough set theory offers a formal theoretical framework for attribute reduction and rule learning from nominal data. However, this model is not applicable to numerical data, which widely exist in real-world applications. In this work, we extend this framework to numerical feature spaces by replacing partition of universe with neighborhood covering and derive a neighborhood covering reduction based approach to extracting rules from numerical data. We first analyze the definition of covering reduction and point out its advantages and disadvantages. Then we introduce the definition of relative covering reduction and develop an algorithm to compute it. Given a feature space, we compute the neighborhood of each sample and form a neighborhood covering of the universe, and then employ the algorithm of relative covering reduction to the neighborhood covering, thus derive a minimal covering rule set. Some numerical experiments are presented to show the effectiveness of the proposed technique.

Axiomatization and conditions for neighborhoods in a covering to form a partition

In this paper, we study the axiomatic issue of a type of covering upper approximation operations. This issue was proposed as an open problem. We also further some known results by using only a single covering approximation operator to characterize the conditions for neighborhood { N( x): x ∈ U} to form a partition of universe U.

Universal partitioning of the hierarchical fold network of 50-residue segments in proteins

BackgroundSeveral studies have demonstrated that protein fold space is structured hierarchically and that power-law statistics are satisfied in relation between the numbers of protein families and protein folds (or superfamilies). We examined the internal structure and statistics in the fold space of 50 amino-acid residue segments taken from various protein folds. We used inter-residue contact patterns to measure the tertiary structural similarity among segments. Using this similarity measure, the segments were classified into a number (Kc) of clusters. We examined various Kc values for the clustering. The special resolution to differentiate the segment tertiary structures increases with increasing Kc. Furthermore, we constructed networks by linking structurally similar clusters.ResultsThe network was partitioned persistently into four regions for Kc ≥ 1000. This main partitioning is consistent with results of earlier studies, where similar partitioning was reported in classifying protein domain structures. Furthermore, the network was partitioned naturally into several dozens of sub-networks (i.e., communities). Therefore, intra-sub-network clusters were mutually connected with numerous links, although inter-sub-network ones were rarely done with few links. For Kc ≥ 1000, the major sub-networks were about 40; the contents of the major sub-networks were conserved. This sub-partitioning is a novel finding, suggesting that the network is structured hierarchically: Segments construct a cluster, clusters form a sub-network, and sub-networks constitute a region. Additionally, the network was characterized by non-power-law statistics, which is also a novel finding.ConclusionMain findings are: (1) The universe of 50 residue segments found here was characterized by non-power-law statistics. Therefore, the universe differs from those ever reported for the protein domains. (2) The 50-residue segments were partitioned persistently and universally into some dozens (ca. 40) of major sub-networks, irrespective of the number of clusters. (3) These major sub-networks encompassed 90% of all segments. Consequently, the protein tertiary structure is constructed using the dozens of elements (sub-networks).

On the Universal Partition Theorem for 4-Polytopes

By means of sign-patterns any finite family of polynomials induces a decomposition of R n into basic semialgebraic sets. In case of integer coefficients the latter decomposition roughly appears to be a partition into realization spaces of 4 -polytopes. The latter is stated by the Universal Partition Theorem for 4 -polytopes by Richter-Gebert. The present paper presents a different proof. As its main tool, the von Staudt polytope is introduced. The von Staudt polytope constitutes the polytopal equivalent of the well-known von Staudt constructions for point configurations. With the aid of the von Staudt polytope the original ideas of universality theory can be directly applied to the polytopal case. Moreover, a new method for representing real values (on a computation line) by polytopal means is presented. This method implies a bundling strategy in order to duplicate the encoded information. Based on this approach, the following complexity result is obtained. The incidence code of a polytope, exhibiting a realization space equivalent to a given semialgebraic set, can be computed in the same time that it requires to generate the defining polynomial system.

The universal partition theorem for oriented matroids

We consider realization spaces of a family of oriented matroids of rank three as point configurations in the affine plane. The fundamental problem arises as to which way these realization spaces partition their embedding space. The Universal Partition Theorem roughly states that such a partition can be as complicated as any partition of ℝ n into elementary semialgebraic sets induced by an arbitrary finite set of polynomials in ℤ[X]. We present the first proof of the Universal Partition Theorem. In particular, it includes the first complete proof of the so-called Universality Theorem.

DOUBLE SCALING LIMIT IN O(N) VECTOR MODELS IN D DIMENSIONS

Using the standard 1/N expansion, we study O(N) vector models in D dimensions with an arbitrary potential. We limit ourselves to renormalizable theories. We show that there exists a value of the coupling constant corresponding to a critical point and that a double scaling limit can be performed as in D=0 and in the case of matrix models in D=0, 1. For D=1 the theory is renormalizable with an arbitrary potential and we find in general a hierarchy of critical theories labeled by an integer k. The universal partition function obtained in the double scaling limit is constructed. Finally, we show that the critical behaviour of those models is the same as a branched polymer model recently constructed by Ambjørn, Durhuus and Jónsson.

Double-scaling limit in supersymmetric O(N) vector models.

Using the standard $\frac{1}{N}$ expansion, we study supersymmetric $\mathrm{O}(N)$ vector models with an arbitrary potential in zero dimensions and discuss the nature and form of the critical behavior. We show that a double-scaling limit exists as in the case of matrix models and in bosonic vector models. We find in general a hierarchy of critical supersymmetric theories labeled by an integer $k$. The universal partition function of the $k\mathrm{th}$ theory is constructed from the effective action in the double-scaling limit.