Cycles Of Different Lengths Research Articles

Edge-disjoint properly colored cycles in edge-colored complete graphs

In an edge-colored graph G, let dmon(v) denote the maximum number of edges with the same color incident with a vertex v in G, called the monochromatic-degree of v. The maximum value of dmon(v) over all vertices v∈V(G) is called the maximum monochromatic-degree of G, denoted by Δmon(G). Li et al. in 2019 conjectured that every edge-colored complete graph G of order n with Δmon(G)≤n−3k+1 contains k vertex-disjoint properly colored (PC for short) cycles of length at most 4, and they showed that the conjecture holds for k=2. Han et al. showed that every edge-colored complete graph G of order n with Δmon(G)≤n−2k contains k PC cycles of different lengths. They further got the condition Δmon(G)≤n−6 for the existence of two vertex-disjoint PC cycles of different lengths. In this paper, we consider the problems of the existence of edge-disjoint PC cycles of length at most 4 (different lengths) in an edge-colored complete graph G of order n.

Properly colored cycles of different lengths in edge-colored complete graphs

A cycle in an edge-colored graph is called properly colored if all of its adjacent edges have distinct colors. Let Knc be an edge-colored complete graph with n vertices and let k be a positive integer. Denote by Δmon(Knc) the maximum number of edges of the same color incident with a vertex of Knc. In this paper, we show that (i) if Δmon(Knc)⩽n−2k, then Knc contains k properly colored cycles of different lengths and the bound is sharp; (ii) if Δmon(Knc)⩽n−2k+1−2k+4, then Knc contains k vertex-disjoint properly colored cycles of different lengths; in particular, Δmon(Knc)⩽n−6 suffices for the existence of two vertex-disjoint properly colored cycles of different lengths.

Vertex-Disjoint Cycles of Different Lengths in Local Tournaments

Vertex-Disjoint Cycles of Different Lengths in Local Tournaments

Seasonal variations in daily data: An application to air passenger arrivals

The aim of this paper is to describe and compare seasonal effects in daily air passenger arrivals. Multiple seasonal cycles of different lengths are usually observed in daily time series. To model weekly cycles over a short and fixed seasonal period, conventional formulations can be applied. However, the length of yearly and, above all, monthly seasonal cycles is not fixed. Yet, whatever the lengths of the seasonal periods, seasonal cycles can be modelled by using evolving spline functions in such a way that a seasonal effect at a proportion of the seasonal period is defined as a non-fixed parametric formulation of this proportion. Thus, restricted evolving spline models are useful to model this type of seasonal variation. The areas under the splines can measure changes in the magnitude of seasonal variations over time and can be used to compare the relevance of seasonal variations for different seasonal periods or different time series. This proposal is illustrated by applying it to daily series of air passengers arriving in the Canary Islands and at the rest of Spain's airports.

Structure-Activity Relationship Investigations of Novel Constrained Chimeric Peptidomimetics of SOCS3 Protein Targeting JAK2.

SOCS3 (suppressor of cytokine signaling 3) protein suppresses cytokine-induced inflammation and its deletion in neurons or immune cells increases the pathological growth of blood vessels. Recently, we designed several SOCS3 peptidomimetics by assuming as template structures the interfacing regions of the ternary complex constituted by SOCS3, JAK2 (Janus Kinase 2) and gp130 (glycoprotein 130) proteins. A chimeric peptide named KIRCONG chim, including non-contiguous regions demonstrated able to bind to JAK2 and anti-inflammatory and antioxidant properties in VSMCs (vascular smooth muscle cells). With the aim to improve drug-like features of KIRCONG, herein we reported novel cyclic analogues bearing different linkages. In detail, in two of them hydrocarbon cycles of different lengths were inserted at positions i/i+5 and i/i+7 to improve helical conformations of mimetics. Structural features of cyclic compounds were investigated by CD (Circular Dichroism) and NMR (Nuclear Magnetic Resonance) spectroscopies while their ability to bind to catalytic domain of JAK2 was assessed through MST (MicroScale Thermophoresis) assay as well as their stability in biological serum. Overall data indicate a crucial role exerted by the length and the position of the cycle within the chimeric structure and could pave the way to the miniaturization of SOCS3 protein for therapeutic aims.

Questioning the seasonality of SARS-COV-2: a Fourier spectral analysis

ObjectivesTo investigate the hypothesis of a seasonal periodicity, driven by climate, in the contagion resurgence of COVID-19 in the period February 2020–December 2021.DesignAn observational study of 30 countries from different...

Disjoint Cycles of Different Lengths in 3-Regular Digraphs

Disjoint Cycles of Different Lengths in 3-Regular Digraphs

Vertex-disjoint rainbow cycles in edge-colored graphs

Let G be an edge-colored graph of order n. The color-neighborhood of a vertex u of G is the set of colors of the edges incident with u in G, denoted by CNG(u), or CN(u) for short. A subgraph F of G is called rainbow if any two edges of F have distinct colors. In this paper, we first give a sufficient condition for the existence of rainbow cycles by using color-neighborhood unions of pairs of vertices in G. In 2019, Fujita et al. showed that G contains k vertex-disjoint rainbow cycles if |CN(x)∪CN(y)|≥n/2+64k+1 for any two vertices x,y of G. We obtain a result that G contains k vertex-disjoint rainbow cycles if |CN(x)∪CN(y)|≥n/2+18k+1 for any two vertices x,y of G. Furthermore, we give better bounds for k=2,3. Finally, we show that G contains two vertex-disjoint rainbow cycles of different lengths if |CN(x)∪CN(y)|≥2n/3+6 for every pair of vertices x,y of G.

Vertex-disjoint cycles of different lengths in multipartite tournaments

We show in this paper that every strong k-partite tournament D=(V,A) with k≥3 and minimum out-degree 3, except the digraphs D73 and D83 which are defined in the introduction of this paper, contains two vertex-disjoint directed cycles of different lengths.

Spectral factor models

We represent risk factors as sums of orthogonal components capturing fluctuations with cycles of different length. The representation leads to novel spectral factor models in which systematic risk is allowed—without being forced—to vary across frequencies. Frequency-specific systematic risk is captured by a notion of spectral beta. We show that traditional factor models restrict the spectral betas to be constant across frequencies. The restriction can hide horizon-specific pricing effects that spectral factor models are designed to reveal. We illustrate how the methods may lead to economically meaningful dimensionality reduction in the factor space.

Tournaments and Bipartite Tournaments without Vertex Disjoint Cycles of Different Lengths

M. A. Henning and A. Yeo conjectured in [SIAM J. Discrete Math., 26 (2012), pp. 687--694] that a bipartite digraph of minimum out-degree at least 3 contains two vertex disjoint directed cycles of different lengths. In this paper, we disprove this conjecture. Further, we classify strong tournaments and strong bipartite tournaments of minimum out-degree 3 without two vertex disjoint directed cycles of different lengths.

A discrete/continuous time resource competition model and its implications

We use a mixed time model to study the dynamics of a system consisting of two consumers that reproduce only in annual birth pulses, possibly at different times, with interaction limited to competition for a resource that reproduces continuously. Ecological theory predicts competitive exclusion; this expectation is met under most circumstances, the winner being the species with the greater ‘power’, defined as the time average consumer level at the fixed point. Instability of that fixed point for the stronger competitor slightly weakens its domination, so that a resident species with an unstable fixed point can sometimes be invaded by a slightly weaker species, leading ultimately to coexistence. Differences in birth pulse times can lead to qualitatively different long-term coexistence behaviour, including cycles of different lengths or chaos. We also determine conditions under which the timing of an annual pulse of a toxin can change the balance of power.

Human babesiosis: recent advances and future challenges.

As human babesiosis caused by apicomplexan parasites of the Babesia genus is associated with transfusion-transmitted illness and relapsing disease in immunosuppressed populations, it is important to report novel findings relating to parasite biology that may be responsible for such pathology. Blood screening tools recently licensed by the FDA are also described to allow understanding of their impact on keeping the blood supply well tolerated. Reports of tick-borne cases within new geographical regions such as the Pacific Northwest of the USA, through Eastern Europe and into China are also on the rise. Novel features of the parasite lifecycle that underlie the basis of parasite persistence have recently been characterized. These merit consideration in deployment of both detection, treatment and mitigation tools such as pathogen inactivation technology. The impact of new blood donor screening tests in reducing transfusion transmitted babesiosis is discussed. New Babesia species have been identified globally, suggesting that the epidemiology of this disease is rapidly changing, making it clear that human babesiosis is a serious public health concern that requires close monitoring and effective intervention measures. Unlike other erythrocytic parasites, Babesia exploits unconventional lifecycle strategies that permit host cycles of different lengths to ensure survival in hostile environments. With the licensure of new blood screening tests, incidence of transfusion transmission babesiosis has decreased.

Planning approaches for stochastic capacitated lot-sizing with service level constraints

We investigate a stochastic capacitated lot-sizing problem whose optimal solution requires the integration of dynamic safety stock planning into lot-sizing. Then, we introduce an integrated mixed-integer linear program with service-level constraints. The integrated model endogenously sets dynamic safety stocks over replenishment cycles of different lengths determined by the model. Since there is limited capacity, soft service-level constraints are introduced to guarantee a feasible solution. In the experimental study, we compare the performance of the integrated model to the stochastic dynamic program and the widely-used sequential approach. If available capacity increases, the integrated model closes the gap to the lower bound approximated by using a stochastic dynamic program. If capacity is limited, the integrated model outperforms the sequential approach because it yields identical service levels with lower inventories. However, in the case of sufficient flexibility (capacity), we identify a major shortcoming of the integrated models: They can generate excessive safety stock if the re-planning opportunities under rolling horizon planning are ignored. To overcome this problem, we extend the integrated model to account for those re-planning opportunities.

A decomposition for digraphs with minimum outdegree 3 having no vertex disjoint cycles of different lengths

A decomposition for digraphs with minimum outdegree 3 having no vertex disjoint cycles of different lengths

Stacked book graphs are cycle-antimagic

A family of subgraphs of a finite, simple and connected graph $G$ is called an edge covering of $G$ if every edge of graph $G$ belongs to at least one of the subgraphs. In this manuscript, we define the edge covering of a stacked book graph and its uniform subdivision by cycles of different lengths. If every subgraph of $G$ is isomorphic to one graph $H$ (say) and there is a bijection $\phi:V(G)\cup E(G) \to \{1, 2, \dots, |V(G)|+|E(G)| \}$ such that $wt_{\phi}(H)$ forms an arithmetic progression then such a graph is called $(\alpha, d)$-$H$-antimagic. In this paper, we prove super $(\alpha, d)$-cycle-antimagic labelings of stacked book graphs and $r$ subdivided stacked book graph.

On 3-regular digraphs of girth 4

We raise the conjecture that every 3-regular digraph, except the digraphs D73, D83 and D2n2 for every integer n≥2, which are defined in the introduction of the paper, contains two vertex disjoint directed cycles of different lengths and give support for this conjecture by proving that every 3-regular digraph of girth 4 contains two vertex disjoint directed cycles of different lengths.

Path integral Monte Carlo simulation of degenerate electrons: Permutation-cycle properties.

Being motivated by the surge of fermionic quantum Monte Carlo simulations at finite temperature, we present a detailed analysis of the permutation-cycle properties of path integral Monte Carlo (PIMC) simulations of degenerate electrons. Particular emphasis is put onto the uniform electron gas in the warm dense matter regime. We carry out PIMC simulations of up to N = 100 electrons and investigate exchange-cycle frequencies, which are found not to follow any simple exponential law even in the case of ideal fermions due to the finite size of the simulation box. Moreover, we introduce a permutation-cycle correlation function, which allows us to analyze the joint probability to simultaneously find cycles of different lengths within a single configuration. Again, we find that finite-size effects predominate the observed behavior. Finally, we briefly consider an inhomogeneous system, namely, electrons in a 2D harmonic trap. We expect our results to be of interest for the further development of fermionic PIMC methods, in particular, to alleviate the notorious fermion sign problem.

Global Financial Cycles Since 1880

With the aim to provide a detailed understanding of global financial cycles and their relevance over time, we analyse co-movement in credit, house prices, equity prices, and interest rates across 17 advanced economies over 130 years. Using a time-varying dynamic factor model, we observe global co-movement across financial variables as well as variable-specific global cycles of different lengths and amplitudes. Global cycles have gained relevance over time. For equity prices, they now constitute the main driver of fluctuations in most countries. Global cycles in credit and housing have become much more pronounced and protracted since the 1980s, but their relevance increased for a sub-group of financially open and developed economies only. Panel regressions indicate that a country’s susceptibility to global financial cycles tends to increase with financial openness and financial integration, the extent of mortgage-related lending, and the efficiency of stock markets. Understanding the cross-country heterogeneity in financial market characteristics therefore matters for the design of appropriate financial stabilization policies across countries and sectors.

Minimum fundamental cycle basis of some bipartite graphs

We determine the number of cycles of different lengths in the minimum fundamental cycle basis of some bipartite graphs with centralized spanning trees. As applications, we characterize the minimum fundamental cycle basis of some (n−k)-regular balanced graphs with order 2n.