Fundamental Cycle Research Articles

The cycle’s structure of embedded graphs in surfaces

In this paper, the cycle’s structure of embedded graphs in surfaces are studied. According to the method of fundamental cycles, the set C (C contains all shortest) is found. A undirected graph G with n vertices has at most O(n5) many shortest cycles; If the shortest cycle of G is odd cycle, then G has at most O(n3) many shortest cycles; If G has been embedded in a surface Sg (Ng, g is a constant), then it has at most O(n3) shortest cycles, moreover, if the shortest cycle of G is odd cycle, then, G has at most O(n2) many shortest cycles. We can find a cycle base of G, the number of odd cycles of G, the number of even cycles of G, the number of contractible cycles of G, the number of non-contractible cycles of G, are all decided. If the ∏-embedded graph G has ∏-twosided cycles, then, C contains a shortest ∏-twosided cycle of G, there is a polynomially bounded algorithm that finds a shortest ∏-twosided cycle of a ∏-embedded graph G, the new and simple solutions about the open problem of Bojan Mohar and Carsten Thomassen are obtained.

Spanning trees with nonseparating paths

We consider questions related to the existence of spanning trees in connected graphs with the property that, after the removal of any path in the tree, the graph remains connected. We show that, for planar graphs, the existence of trees with this property is closely related to the Hamiltonicity of the graph. For graphs with a 1- or 2-vertex cut, the Hamiltonicity also plays a central role. We also deal with spanning trees satisfying this property restricted to paths arising from fundamental cycles. The cycle space of a graph can be generated by the fundamental cycles of every spanning tree, and Tutte showed that, for a 3-connected graph, it can be generated by nonseparating cycles. We are also interested in the existence of a fundamental basis consisting of nonseparating cycles.

THE FUNERAL AND MEMORIAL RITES OF THE LUDICS (BASED ON THE R. F. TAROEVA’S FIRST ETHNOLOGY EXPEDITION )

The paper deals with the analysis of the funeral and memorial rites of Ludic Karelians of the Kondopozhsky District. The information of the rites is founded on the materials of the first ethnological expedition undertaken in 1956 under the leadership of R. F. Taroeva. The paper treats of such fundamental cycles of the funeral rites as preparing body for burial, funeral and memorial rites. It is concluded that funeral and memorial rites, which existed in the Ludics until the 1950s, had components of different origins: folk and Christianized components as well as the ones that originated under the influence of the urban environment components.

Direct Regular Sampled Pulse Width Modulation Technique for a Three-Phase Current Source Inverter

This paper proposes a new regular sampled pulse width modulation (PWM) for three-phase current source inverters. The theoretical basis of the proposed modulation strategy is described, including dwell time calculations and switching sequence selection. This strategy is well suited for digital implementation, and enjoys all the flexibilities and degree of freedoms as in space vector modulation. In addition, it ensures a minimum number of switching transitions per fundamental cycle, unlike other PWM methods. It is therefore promising for high-power medium-voltage applications. The validity of the proposed modulation strategy has been confirmed using simulation and experimentation. To furthermore substantiate the superiority of the proposed modulation strategy against other PWM methods, its performance is compared to sinusoidal PWM, selective harmonic elimination, and space vector modulation.

Criteria-Based Modulation for Multilevel Inverters

Pulse width modulation schemes are aimed at adjusting the fundamental component while reducing the harmonic content of an inverter output voltage or current. This paper addresses the topic of optimal inverter operation in reference to a given objective function. The objective function could embody either a single performance criterion, such as voltage or current total harmonic distortion (THD), or a weighted sum of multiple criteria. The proposed method ensures primacy of the chosen solution while imposing no restriction over its modulation index. In particular, operating the inverter by the chosen solution would result in performances superior to any other modulation scheme commutating in an equal number of switching angles per fundamental cycle. The proposed method allows for the consideration of practical inverter constraints and prevents the possibility of impractical switching sequence. A detailed investigation of the method is given, accompanied by two practical cases minimizing, respectively, phase-voltage THD and line-current THD of a three-level inverter. Selected simulation and experimental results are presented to validate the theoretical part.

Representation of the kinematic topology of mechanisms for kinematic analysis

Abstract. The kinematic modeling of multi-loop mechanisms requires a systematic representation of the kinematic topology, i.e. the arrangement of links and joints. A linear graph, called the topological graph, is used to this end. Various forms of this graph have been introduced for application in mechanism kinematics and multibody dynamics aiming at matrix formulations of the governing equations. For the (higher-order) kinematic analysis of mechanisms a simple yet stringent representation of the topological information is often sufficient. This paper proposes a simple concept and notation for use in kinematic analysis. Upon a topological graph, an order relation of links and joints is introduced allowing for recursive computation of the mechanism configuration. An ordering is also introduced on the topologically independent fundamental cycles. The latter is indispensable for formulating generically independent loop closure constraints. These are presented for linkages with only lower pairs, as well as for mechanisms with one higher kinematic pair per fundamental cycle. The corresponding formulation is known as cut-body and cut-joint approach, respectively.

Trigonometric functions representing annual winter coat shedding and regrowth in Angus cows

Subjective scores (n=2603) representing (1) the shedding and regrowth of winter coat and (2) total quantity of hair were recorded monthly for 2yr for 135 Angus cows. Shedding scores of 1 indicated summer coats (all winter coat shed) and 5 indicated complete winter coats. Quantity scores of 1 and 5 indicated minimal and maximal amounts of hair in the coat, respectively. Scores of 2 through 4 for respective traits indicated intermediate conditions. A trigonometric function representing a sinusoid process was fitted to the residuals of scores across time: Asin[B(t−C)]+D, where A represents the height of peaks in the oscillatory function above a centralized baseline in the Cartesian plane; B represents the angular frequency, that is, the rate of change of scores across a complete fundamental cycle of the process; C represents the horizontal shift in the cycle; D represents the vertical offset of the function. The time dimension in months is represented as t. Parameters for this function were estimated for the two traits using least squares nonlinear regression procedures (1) across all data, (2) within cow age categories, and (3) within groups of cows representing distinct maternal lineages. In all cases, parameters representing amplitude (A) and angular frequency (B) seemed to be estimated most reliably (as indicated by magnitude of SE) and the parameter representing the vertical offset seemed to be estimated least reliably. The numerically larger estimate of the amplitude parameter (A) for winter coat shedding and regrowth score relative to the quantity of hair score suggested that it better characterized the process, as well as differences among cow age groups or maternal lineages. For both traits within all groupings of records the parameter representing the horizontal phase shift (C) appeared to be most informative: curves for younger cows were shifted to the right in the time space, indicating later shedding of winter coat. The phase shift parameter also best characterized differences in the process for cows in different maternal lineages; however, numerical differences in the parameter estimates representing amplitude (A) and angular frequency (B) also appeared to be responsible for the distinctiveness of group curves. Curves visually represented the shedding of winter coats (April–July in the time parameter space) better than the winter regrowth process. There may be value in considering parameters of such curves in some genetic improvement strategies for enhancing cow adaptability to local environmental conditions.

A New Method of Power Arithmetic for Parallel Inverter

To overcome the one fundamental cycle delay of the conventional power arithmetic under the load change, a new method of power arithmetic is proposed, which rebuilds the sinusoidal signal only using the last-value and next value of signal in discrete domain. Thus, it is able to fast calculate power value and can obtain the true power value only in one sampling cycle. Moreover, it occupies much smaller DSP space and cuts down computing process, as the sine and cosine tables are cancelled. The high precision of proposed method has validated through comparison with the ideal and simulation values of active, reactive power. Experimental results from a two-75-kVA- inverters system show the proposed method is practicable.

Human β-cell proliferation and intracellular signaling: part 3.

This is the third in a series of Perspectives on intracellular signaling pathways coupled to proliferation in pancreatic β-cells. We contrast the large knowledge base in rodent β-cells with the more limited human database. With the increasing incidence of type 1 diabetes and the recognition that type 2 diabetes is also due in part to a deficiency of functioning β-cells, there is great urgency to identify therapeutic approaches to expand human β-cell numbers. Therapeutic approaches might include stem cell differentiation, transdifferentiation, or expansion of cadaver islets or residual endogenous β-cells. In these Perspectives, we focus on β-cell proliferation. Past Perspectives reviewed fundamental cell cycle regulation and its upstream regulation by insulin/IGF signaling via phosphatidylinositol-3 kinase/mammalian target of rapamycin signaling, glucose, glycogen synthase kinase-3 and liver kinase B1, protein kinase Cζ, calcium-calcineurin–nuclear factor of activated T cells, epidermal growth factor/platelet-derived growth factor family members, Wnt/β-catenin, leptin, and estrogen and progesterone. Here, we emphasize Janus kinase/signal transducers and activators of transcription, Ras/Raf/extracellular signal–related kinase, cadherins and integrins, G-protein–coupled receptors, and transforming growth factor β signaling. We hope these three Perspectives will serve to introduce these pathways to new researchers and will encourage additional investigators to focus on understanding how to harness key intracellular signaling pathways for therapeutic human β-cell regeneration for diabetes.

Finding Shorter Cycles in a Weighted Graph

In this paper we investigate the structures of short cycles in a weighted graph. By Thomassen's $$3$$3-path-condition theory (Thomassen in J Comb Theory Ser 48:155---177, 1990), it is easy to find a shortest cycle in a collection of cycles beyond a subspace of the cycle space of a graph. What is more difficult for one to do is to find a shortest cycle within a subspace of the cycle space in polynomial time. By using the Dijkstra's algorithm (Dijkstra in Numer Math 1:55---61, 1959) we find a collection $$\mathcal {C}$$C of cycles containing many types of short cycles within a given subspace of the cycle space of a graph and this implies a polynomial time algorithm (called extended fundamental cycle algorithm) to locate all the possible shortest cycles in a weighted graph. In the case of unweighted graphs, the algorithm may also find every shortest even cycle in a graph, this greatly improved a result of Grotschel and Pulleyblank (Oper Res Lett 1:23---27, 1981/82), Monien (Computing 31:355---369, 1983), Yuster and Zwick (SIAM J Discrete Math 10:209---222, 1997). In fact, our algorithm shows that there are at most $$O(n^4)$$O(n4) many such short cycles in an unweighted graph of order $$n$$n. Further more, our fundamental cycle method may find a minimum cycle base (or simply MCB as some scholars named) in the cycle space of a graph. Since the structure of MCB's is unique (Ren and Deng in Discrete Math 307:2654---2660, 2007), this shows that, in the sense, cycles in a MCB are nearly-fundamental (i.e., each element in a MCB is a sum of at most two fundamental cycles). This provides a new way to study MCB.

Nucleation and Growth of Lithium Peroxide in the Li/O2 Cell

The aprotic Li–O2 battery offers a vast improvement in theoretical energy density up to ten times that of current Li-ion batteries, but still suffers from shortcomings in cell and material design. Some of these shortcomings stem from the large gap in understanding between fundamental studies and cell cycling experiments. In particular, it is known from computational studies that the solid Li2O2 discharge product is an electronic insulator, but SEM images of discharged cathodes show particles of Li2O2 much larger than what electron conduction and tunneling would allow. In addition, the shape of the discharge curves does not match the expected exponential resistance rise of a cell limited by electron tunneling. In order to bridge Li2O2 properties with experimental observations, we developed a model in which Li2O2 forms as discrete particles on the cathode surface by using a combination of Kolmogorov’s statistical phase transformation theory and the atomistic nucleation theory. Nucleation rate was modeled according to a two-step process involving formation of a LiO2 intermediate. Despite its relative simplicity, the proposed model provides a near-quantitative description of empirically observed discharge curves (Figure 1). We find that the sudden potential drop at the end of discharge is caused by the reduction in active surface area as Li2O2 covers the cathode surface. Thus, the extra overpotential gained during discharge is the kinetic overpotential of the ORR rather than an ohmic overpotential through the Li2O2 bulk. This model can be used as a guide for cathode and electrolyte design, by maximizing the amount of Li2O2 that can be collected for a given amount of electrochemically active surface area. One strategy is to promote the growth of larger Li2O2 particles. For cathodes, this means reducing the rate of nucleation by having a higher nucleation energy barrier or a lower concentration of active sites. For electrolytes, this means solvating the LiO2 intermediate to promote the superoxide disproportionation pathway. In principle, the general form of this model is applicable to any electrochemical cell that produces a solid passivation layer. Figure 1: (a) Empirically observed discharge curves (symbols), compared with fit of the nucleation and growth model (lines). (b) Analysis of model parameters shows that they are independent of operating conditions. Figure 1

Scheduling cluster tools for concurrent processing of two wafer types with PM sharing

We examine cyclic scheduling of single-armed and dual-armed cluster tools that concurrently process two wafer types by sharing a process module (PM). Because a PM is shared by two different wafers, the backward and swap sequences, which are prevalently used for single-armed and dual-armed tools without such complexity, respectively, are not effective. We therefore propose new sequences, called alternating backward and alternating swap sequences, for steady cycles of single-armed and dual-armed tools, respectively. We then develop optimality conditions for which the proposed sequences achieve the minimum cycle times in a fundamental cycle, and show that the optimality conditions hold for most practical cases. We also develop a condition for which a shared PM becomes the bottleneck and hence the PM sharing increases the cycle time. For general cycles, we propose heuristic scheduling methods that combine both the alternating backward (or swap) sequence and the conventional backward (or swap) sequence. Finally, we experimentally verify the efficiency and effectiveness of the proposed algorithm for dual-armed cluster tools.

Re-replication of a centromere induces chromosomal instability and aneuploidy.

The faithful inheritance of chromosomes during cell division requires their precise replication and segregation. Numerous mechanisms ensure that each of these fundamental cell cycle events is performed with a high degree of fidelity. The fidelity of chromosomal replication is maintained in part by re-replication controls that ensure there are no more than two copies of every genomic segment to distribute to the two daughter cells. This control is enforced by inhibiting replication initiation proteins from reinitiating replication origins within a single cell cycle. Here we show in Saccharomyces cerevisiae that re-replication control is important for the fidelity of chromosome segregation. In particular, we demonstrate that transient re-replication of centromeric DNA due to disruption of re-replication control greatly induces aneuploidy of the re-replicated chromosome. Some of this aneuploidy arises from missegregation of both sister chromatids to one daughter cell. Aneuploidy can also arise from the generation of an extra sister chromatid via homologous recombination, suggesting that centromeric re-replication can trigger breakage and repair events that expand chromosome number without causing chromosomal rearrangements. Thus, we have identified a potential new non-mitotic source of aneuploidy that can arise from a defect in re-replication control. Given the emerging connections between the deregulation of replication initiation proteins and oncogenesis, this finding may be relevant to the aneuploidy that is prevalent in cancer.

Subcycle Voltage Dip Classification Using Matrix Pencil Method With Ellipse Fitting Algorithm

We have developed a technique using the matrix pencil method (MPM), which was augmented with an ellipse fitting algorithm, that can classify three-phase voltage dips only using subcycle voltage data. This technique uses the MPM to extract the fundamental frequency components and reconstructs the fundamental voltage space vector that often changes into an ellipse during a fault. This ellipse's parameters are then estimated by an ellipse fitting algorithm to classify the dip. We have demonstrated that this technique can differentiate between highly distorted and similar voltage dips only using a quarter-cycle of data, which is equivalent to 5 ms in a 50-Hz alternating-current system. This method is further improved by prefiltering and downsampling the data to reduce the computation time and is implemented on a National Instruments CompactRIO platform. This system classified the dip in real time at about 10-12 ms after fault detection when tested with reproduced fault voltage waveforms amplified to a voltage level of 415 V. Our method thus executes faster than the conventional method of the fast Fourier transform that requires at least a full fundamental cycle time of 20 ms. This technique serves as a method of analyzing subcycle voltage dip phenomena and can be potentially extended to other fast subcycle electrical events.

A new hysteresis band current control technique for a shunt active filter

This paper proposes a hysteresis band (HB) current control technique to reduce the power losses in a shunt active filter. During a switching period in the zero-crossing region, the inverter output current flows through a transistor. By changing the direction, it flows through the free-wheeling diode of the same switch in an inverter leg, or vice versa. The shunt active filter current typically has 6 zero-crossing regions during a fundamental frequency cycle. This paper presents a HB current control technique where there is not any switching in these 6 zero-crossing regions per period, which results in reducing the power losses. The experimental results clearly show that the power losses of the shunt active filter are reduced by using the proposed technique.

Online Sensorless Position Estimation for Switched Reluctance Motors Using One Current Sensor

This paper proposes an online sensorless rotor position estimation technique for switched reluctance motors (SRMs) using just one current sensor. It is achieved by first decoupling the excitation current from the bus current. Two phase-shifted pulse width modulation signals are injected into the relevant lower transistors in the asymmetrical half-bridge converter for short intervals during each current fundamental cycle. Analog-to-digital converters are triggered in the pause middles of the dual pulse to separate the bus current for excitation current recognition. Next, the rotor position is estimated from the excitation current, by a current-rise-time method in the current-chopping-control mode in a low-speed operation and a current-gradient method in the voltage-pulse-control mode in a high-speed operation. The proposed scheme requires only a bus current sensor and a minor change to the converter circuit, without a need for individual phase current sensors or additional detection devices, achieving a more compact and cost-effective drive. The performance of the sensorless SRM drive is fully investigated. The simulation and experiments on a 750-W three-phase 12/8-pole SRM are carried out to verify the effectiveness of the proposed scheme.

Enhanced longevity by ibuprofen, conserved in multiple species, occurs in yeast through inhibition of tryptophan import.

The common non-steroidal anti-inflammatory drug ibuprofen has been associated with a reduced risk of some age-related pathologies. However, a general pro-longevity role for ibuprofen and its mechanistic basis remains unclear. Here we show that ibuprofen increased the lifespan of Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster, indicative of conserved eukaryotic longevity effects. Studies in yeast indicate that ibuprofen destabilizes the Tat2p permease and inhibits tryptophan uptake. Loss of Tat2p increased replicative lifespan (RLS), but ibuprofen did not increase RLS when Tat2p was stabilized or in an already long-lived strain background impaired for aromatic amino acid uptake. Concomitant with lifespan extension, ibuprofen moderately reduced cell size at birth, leading to a delay in the G1 phase of the cell cycle. Similar changes in cell cycle progression were evident in a large dataset of replicatively long-lived yeast deletion strains. These results point to fundamental cell cycle signatures linked with longevity, implicate aromatic amino acid import in aging and identify a largely safe drug that extends lifespan across different kingdoms of life.

On minimum average stretch spanning trees in polygonal 2-trees

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. For a polygonal 2-tree on n vertices, we present an algorithm to compute a minimum average stretch spanning tree in O(nlog⁡n) time. This algorithm also finds a minimum fundamental cycle basis in polygonal 2-trees. We show that there is a unique minimum cycle basis in a polygonal 2-tree and it can be computed in linear time.

Analytical evaluation of harmonic distortion factor corresponding to generalised advanced bus‐clamping pulse width modulation

A few advanced bus-clamping pulse width modulation (ABCPWM) methods have been proposed recently for a three-phase inverter. With these methods, each phase is clamped, switched at nominal frequency, and switched at twice the nominal frequency in different regions of the fundamental cycle. This study proposes a generalised ABCPWM scheme, encompassing the few ABCPWM schemes that have been proposed and many more ABCPWM schemes that have not been reported yet. Furthermore, analytical closed-form expression is derived for the harmonic distortion factor corresponding to the generalised ABCPWM. This factor is independent of load parameters. The analytical expression derived here brings out the dependence of root-mean-square (RMS) current ripple on modulation index, and can be used to evaluate the RMS current ripple corresponding to any ABCPWM scheme. The analytical closed-form expression is validated experimentally in terms of measured weighted total harmonic distortion (THD) in line voltage (V-WTHD) and measured THD in line current (I-THD) on a 6 kW induction motor drive.

The theory of ordinal length

Gulliksen, following Bass’s observations, extended the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. We show how to calculate this combinatorial invariant by means of the fundamental cycle of the module, thus linking the lattice of submodules to homological properties of the module. Using this, we equip each module with its canonical topology. From ordinal length, other ordinal-valued invariants can be derived, such as filtration rank.