Cyclic Order Research Articles

Efficient Communication Scheduling for Parameter Synchronization of DML in Data Center Networks

It's common practice to speed up machine learning (ML) training by distributing it across a cluster of computing nodes. Data-parallel distributed ML (DML) training relieves the pressure of computing node; however, the communication traffic introduced during parameter synchronization becomes bottleneck of DML training. Regarding communication bottleneck, we identify two primary causes: high contention of concurrent communication and large volume of redundant transmission in the push and pull stage while synchronizing parameters. To address these issues, we propose a novel Group Stale Synchronous Parallel (GSSP) scheme, which divides the nodes into groups and coordinates groups to synchronize in a circular order. GSSP mitigates network contention and is proven to converge. We provide analysis of the optimal group's number based on bandwidth and buffer size. For reducing traffic redundancy, we propose a multicast-based scheme, which generates multicast trees by minimizing links overlap and allocates transmission rate to multicast flows by solving the min-max optimization problem. Finally, we conduct extensive simulations to evaluate the performance of our proposals. We simulate parameter transmission of All-Reduce and parameter server in Fat-Tree with traffics trace of ML models. Simulation results show that our proposals provide communication-efficiency for DML training by mitigating contention and reducing redundancy.

An informative frequency band identification framework for gearbox fault diagnosis under time-varying operating conditions

The application of informative frequency band identification methods makes it possible to enhance weak damage components in the vibration signals acquired from rotating machines. Some rotating machines (e.g. wind turbines) operate inherently under time-varying operating conditions, however, very few frequency band identification methods have been developed with varying operating conditions in mind. Therefore, in this work, a systematic framework for obtaining consistent feature planes under time-varying operating conditions is proposed. This framework utilises the angle-frequency instantaneous power spectrum and the order-frequency cyclic modulation spectrum to construct feature planes. The kurtogram, the sparsogram, the infogram, the ICS2gram and the log-cycligram are obtained on numerical and experimental datasets acquired under time-varying operating conditions using this framework. In addition to this, we also implement the Informative Frequency Band Identification method using targeted cyclic orders, abbreviated to IFBIαgram, in this framework and compare the performance of this method against the other frequency band identification methods. Ultimately, we found that the feature used in the construction of the IFBIαgram is very well-suited for gear and bearing fault diagnosis under time-varying operating conditions.

On the Uniqueness of Co-circular Four Body Central Configurations

We study central configurations lying on a common circle in the Newtonian four-body problem. Using a topological argument we prove that there is at most one co-circular central configuration for each cyclic ordering of the masses on the circle.

Second order noise shaping for data-weighted averaging technique to improve sigma-delta DAC performance

<p>In general, the noise shaping responses, a cyclic second order response is delivered by the method of data weighted averaging (DWA) in which the output of the digital-to-analog convertor (DAC) is restricted to one of two states. DWA works efficiently for rather low levels of quantizing; it begins presenting considerable difficulties when internal levels of quantizing are extended further. Though, each added bit of internal quantizing causes an exponentially increasing in power dissipation, complexity and size of the DWA logic and the DAC. This gives a controlled seconnd order response accounting for the mismatch of the elements of DAC. The multi-bit DAC is made up of numerous single-bit DACs having values thereof chosen via a digital encoder. This research presents a discussion of the influence of mismatching between unit elements of the Delta-Sigma DAC. This results in a constrained second order response accounting for mismatch of DAC elements. The results of the simulation showed how the effectiveness of DWA method is in reducing band tones. Furthermore, DWA method has proved its efficiency in solving the mismatching of DAC unit elements. The noise of the mismatching elements is enhanced 11 dB at 0.01 with the proposed DWA, thereby enhancing the efficiency of the DAC in comparison to the efficiency of the DAC with no use of the circuit of DWA</p>

Best-response dynamics, playing sequences, and convergence to equilibrium in random games

We show that the playing sequence--the order in which players update their actions--is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random $n$-player $m$-action games under three distinct playing sequences: clockwork sequences (players take turns according to a fixed cyclic order), random sequences, and simultaneous updating by all players. We analytically characterize the convergence properties of the clockwork sequence best-response dynamic. Our key asymptotic result is that this dynamic almost never converges to a pure Nash equilibrium when $n$ and $m$ are large. By contrast, the random sequence best-response dynamic converges almost always to a pure Nash equilibrium when one exists and $n$ and $m$ are large. The clockwork best-response dynamic deserves particular attention: we show through simulation that, compared to random or simultaneous updating, its convergence properties are closest to those exhibited by three popular learning rules that have been calibrated to human game-playing in experiments (reinforcement learning, fictitious play, and replicator dynamics).

On the uniqueness of trapezoidal four-body central configurations

We study central configurations of the Newtonian four-body problem that form a trapezoid. Using a topological argument we prove that there is at most one trapezoidal central configuration for each cyclic ordering of the masses.

An Optimal Algorithm for Strict Circular Seriation

We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between $n$ objects and the goal is to find a circular order of the objects in a manner that is c...

Facial unique-maximum edge and total coloring of plane graphs

An edge coloring of a plane graph is facial if every two facially adjacent edges (i.e., the edges that are adjacent and consecutive in a cyclic order around their common end vertex) receive different colors. A total coloring of a plane graph is facial if every two adjacent vertices, every two facially adjacent edges and every two incident elements receive different colors. A coloring of a plane graph (using linearly ordered color set) is unique-maximum if, for each face, the maximum color on its elements is used exactly once. In the paper it is proven, that every 2-edge-connected plane graph is facially unique-maximum 4-edge-colorable and facially unique-maximum 6-total-colorable, and that the bounds 4 and 6, respectively, are best possible. Furthermore, every plane graph is facially unique-maximum 6-edge-choosable and facially unique-maximum 8-total-choosable.

Counting Hamilton cycles in Dirac hypergraphs

AbstractA tight Hamilton cycle in a k-uniform hypergraph (k-graph) G is a cyclic ordering of the vertices of G such that every set of k consecutive vertices in the ordering forms an edge. Rödl, Ruciński and Szemerédi proved that for $k\ge 3$ , every k-graph on n vertices with minimum codegree at least $n/2+o(n)$ contains a tight Hamilton cycle. We show that the number of tight Hamilton cycles in such k-graphs is ${\exp(n\ln n-\Theta(n))}$ . As a corollary, we obtain a similar estimate on the number of Hamilton ${\ell}$ -cycles in such k-graphs for all ${\ell\in\{0,\ldots,k-1\}}$ , which makes progress on a question of Ferber, Krivelevich and Sudakov.

Юридические курсы как форма ускоренной подготовки кадров судей в период НЭПа

The article is devoted to the problems of professional training of Soviet judges during the new economic policy period. The legal normative base of the organization and functioning of legal courses is analyzed, the dynamics of the personnel of the courts by the level of education is traced. The training of justice staff was carried out at legal courses: the highest one-year, regional six-month, short-term (three-month). Circular orders of the Commissariat of Justice defined the content of the educational program of legal courses, the status of student and their material support. The training allowed students of legal courses to become a judge. The big need for judges and the high staff of the court turnover caused a deficit of student to fill the personnel of the courts. By 1929, only 10 percent of judges had theoretical training – graduated from legal courses.

On the Minimum Size of Hamilton Saturated Hypergraphs

For $1\leq \ell< k$, an $\ell$-overlapping $k$-cycle is a $k$-uniform hypergraph in which, for some cyclic vertex ordering, every edge consists of $k$ consecutive vertices and every two consecutive edges share exactly $\ell$ vertices. A $k$-uniform hypergraph $H$ is $\ell$-hamiltonian saturated if $H$ does not contain an $\ell$-overlapping hamiltonian $k$-cycle but every hypergraph obtained from $H$ by adding one edge does contain such a cycle. Let sat$(N,k,\ell)$ be the smallest number of edges in an $\ell$-hamiltonian saturated $k$-uniform hypergraph on $N$ vertices. In the case of graphs Clark and Entringer showed in 1983 that sat$(N,2,1)=\lceil \tfrac{3N}2\rceil$. The present authors proved that for $k\geq 3$ and $\ell=1$, as well as for all $0.8k\leq \ell\leq k-1$, sat$(N,k,\ell)=\Theta(N^{\ell})$. Here we prove that sat$(N,2\ell,\ell)=\Theta\left(N^\ell\right)$.

Cyclically parallelized treecode for fast computations of electrostatic interactions on molecular surfaces

We study the parallelization of a flexible order Cartesian treecode algorithm for evaluating electrostatic potentials of charged particle systems in which N particles are located on the molecular surfaces of biomolecules such as proteins. When the well-separated condition is satisfied, the treecode algorithm uses a far-field Taylor expansion to compute O(NlogN) particle–cluster interactions to replace the O(N2) particle–particle interactions. The algorithm is implemented using the Message Passing Interface (MPI) standard by creating identical tree structures in the memory of each task for concurrent computing. We design a cyclic order scheme to uniformly distribute spatially-closed target particles to all available tasks, which significantly improves parallel load balancing. We also investigate the parallel efficiency subject to treecode parameters such as Taylor expansion order p, maximum particles per leaf N0, and maximum acceptance criterion θ. This cyclically parallelized treecode can solve interactions among up to tens of millions of particles. However, if the problem size exceeds the memory limit of each task, a scalable domain decomposition (DD) parallelized treecode using an orthogonal recursive bisection (ORB) tree can be used instead In addition to efficiently computing the N-body problem of charged particles, our approach can potentially accelerate GMRES iterations for solving the boundary integral Poisson–Boltzmann equation.

On the cyclic order distribution and partitioning of linear cyclic codes

In this paper, we propose a way to partition any linear cyclic code in its cyclic equivalence classes according to the algebraic structure of the code. Such partition is useful to generate cyclically permutable codes directly from linear cyclic codes. We consider the case where the size of the finite field and the block length of the code are coprimes. Moreover, we present a criterion to construct maximal cyclic order codes.

Finding tight Hamilton cycles in random hypergraphs faster

AbstractIn an r-uniform hypergraph on n vertices, a tight Hamilton cycle consists of n edges such that there exists a cyclic ordering of the vertices where the edges correspond to consecutive segments of r vertices. We provide a first deterministic polynomial-time algorithm, which finds a.a.s. tight Hamilton cycles in random r-uniform hypergraphs with edge probability at least C log3n/n.Our result partially answers a question of Dudek and Frieze, who proved that tight Hamilton cycles exist already for p = ω(1/n) for r = 3 and p = (e + o(1))/n for $r \ge 4$ using a second moment argument. Moreover our algorithm is superior to previous results of Allen, Böttcher, Kohayakawa and Person, and Nenadov and Škorić, in various ways: the algorithm of Allen et al. is a randomized polynomial-time algorithm working for edge probabilities $p \ge {n^{ - 1 + \varepsilon}}$, while the algorithm of Nenadov and Škorić is a randomized quasipolynomial-time algorithm working for edge probabilities $p \ge C\mathop {\log }\nolimits^8 n/n$.

Algebras of Binary Formulas for Compositions of Theories

We consider algebras of binary formulas for compositions of theories both in the general case and as applied to ℵ0-categorical, strongly minimal, and stable theories, linear preorders, cyclic preorders, and series of finite structures. It is shown that edefinable compositions preserve isomorphisms and elementary equivalence and have basicity formed by basic formulas of the initial theories. We find criteria for e-definable compositions to preserve ℵ0-categoricity, strong minimality, and stability. It is stated that e-definable compositions of theories specify compositions of algebras of binary formulas. A description of forms of these algebras is given relative to compositions with linear orders, cyclic orders, and series of finite structures.

Cyclic Topology Enhancing Structural Ordering and Stability of Comb-Shaped Polypeptoid Thin Films against Melt-Induced Dewetting.

We investigated the effect of cyclic chain topology on the molecular ordering and thermal stability of comb-shaped polypeptoid thin films on silicon (Si) substrates. Cyclic and linear poly(N-decylglycine) (PNDG) bearing long n-decyl side chains were synthesized by ring-opening polymerization of N-decylglycine-derived N-carboxyanhydrides. When the spin-coated thin films were subjected to thermal annealing at temperatures above the melting temperature (T > Tm), the cyclic PNDG films exhibited significantly enhanced stability against melt-induced dewetting than the linear counterparts (l-PNDG). When recrystallized at temperatures below the crystallization temperature (T < Tc), the homogeneous c-PNDG films exhibit enhanced crystalline ordering relative to the macroscopically dewetted l-PNDG films. Both cyclic and linear PNDG molecules adopt cis-amide conformations in the crystalline film, which transition into trans-amide conformations upon melting. A top-down solvent leaching treatment of both l/c-PNDG films revealed the formation of an irreversibly physisorbed monolayer with similar thickness (ca. 3 nm) on the Si substrate. The physisorbed monolayers are more disordered relative to the respective thicker crystalline films for both cyclic and linear PNDGs. Upon heating above Tm, the adsorbed c-PNDG chains adopt trans-amide backbone conformation identical with the free c-PNDG molecules in the molten film. By contrast, the backbone conformations of l-PNDG chains in the adsorbed layers are notably different from those of the free chains in the molten film. We postulate that the conformational disparity between the chains in the physically adsorbed layers versus the free chains in the molten film is an important factor to account for the difference in the thermal stability of PNDG thin films. These findings highlight the use of cyclic chain topology to suppress the melt-induced dewetting in polymer thin films.

A population-based gene expression signature of molecular clock phase from a single epidermal sample

BackgroundFor circadian medicine to influence health, such as when to take a drug or undergo a procedure, a biomarker of molecular clock phase is required––one that is easily measured and generalizable across a broad population. It is not clear that any circadian biomarker yet satisfies these criteria.MethodsWe analyzed 24-h molecular rhythms in human dermis and epidermis at three distinct body sites, leveraging both longitudinal (n = 20) and population (n = 154) data. We applied cyclic ordering by periodic structure (CYCLOPS) to order the population samples where biopsy time was not recorded. With CYCLOPS-predicted phases, we used ZeitZeiger to discover potential biomarkers of clock phase.ResultsCircadian clock function was strongest in the epidermis, regardless of body site. We identified a 12-gene expression signature that reported molecular clock phase to within 3 h (mean error = 2.5 h) from a single sample of epidermis––the skin’s most superficial layer. This set performed well across body sites, ages, sexes, and detection platforms.ConclusionsThis research shows that the clock in epidermis is more robust than dermis regardless of body site. To encourage ongoing validation of this putative biomarker in diverse populations, diseases, and experimental designs, we developed SkinPhaser––a user-friendly app to test biomarker performance in datasets (https://github.com/gangwug/SkinPhaser).

Dynamic Covalent Self-Sorting and Kinetic Switching Processes in Two Cyclic Orders: Macrocycles and Macrobicyclic Cages.

Dynamic covalent component self-sorting processes have been investigated for constituents of different cyclic orders, macrocycles and macrobicyclic cages based on multiple reversible imine formation. The progressive assembly of the final structures from dialdehyde and polyamine components involved the generation of kinetic products and mixtures of intermediates which underwent component selection and self-correction to generate the final thermodynamic constituents. Importantly, constitutional dynamic networks (CDNs) of macrocycles and macrobicyclic cages were set up either from separately prepared constituents or by in situ assembly from their components. Over time, these CDNs underwent conversion from a kinetically trapped out-of-equilibrium distribution of constituents to the thermodynamically self-sorted one through component exchange in different dimensional orders.

On compatible triangulations with a minimum number of Steiner points

Two vertex-labelled polygons are compatible if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations—for every face, the clockwise cyclic order of vertices on the boundary must be the same. It is known that every pair of compatible n-vertex polygonal regions can be extended to compatible triangulations by adding O(n2) Steiner points. Furthermore, Ω(n2) Steiner points are sometimes necessary, even for a pair of polygons. Compatible triangulations provide piecewise linear homeomorphisms and are also a crucial first step in morphing planar graph drawings, aka “2D shape animation.” An intriguing open question, first posed by Aronov, Seidel, and Souvaine in 1993, is to decide if two compatible polygons have compatible triangulations with at most k Steiner points. In this paper we prove the problem to be NP-hard for polygons with holes. The question remains open for simple polygons.

Extensions of partial cyclic orders and consecutive coordinate polytopes

We introduce several classes of polytopes contained in $[0,1]^n$ and cut out by inequalities involving sums of consecutive coordinates. We show that the normalized volumes of these polytopes enumerate circular extensions of certain partial cyclic orders. Among other things this gives a new point of view on a question popularized by Stanley. We also provide a combinatorial interpretation of the Ehrhart $h^*$-polynomials of some of these polytopes in terms of descents of total cyclic orders. The Euler numbers, the Eulerian numbers and the Narayana numbers appear as special cases.