Total and forcing total edge-to-vertex monophonic number of a graph

For a connected graph \(G = \left( V,E\right) \), a set \(S\subseteq E(G)\) is called a total edge-to-vertex monophonic set of a connected graph G if the subgraph induced by S has no isolated edges. The total edge-to-vertex monophonic number \(m_{tev}(G)\) of G is the minimum cardinality of its total edge-to-vertex monophonic set of G. The total edge-to-vertex monophonic number of certain classes of graphs is determined and some of its general properties are studied. Connected graphs of size \(q \ge 3 \) with total edge-to-vertex monophonic number q is characterized. It is shown that for positive integers \(r_{m},d_{m}\) and \(l\ge 4\) with \(r_{m}< d_{m} \le 2 r_{m}\), there exists a connected graph G with \(\textit{rad}_ {m} G = r_{m}\), \(\textit{diam}_ {m} G = d_{m}\) and \(m_{tev}(G) = l\) and also shown that for every integers a and b with \(2 \le a \le b\), there exists a connected graph G such that \( m_{ev}\left( G\right) = b\) and \(m_{tev}(G) = a + b\). A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing total edge-to-vertex monophonic number of S, denoted by \(f_{tev}(S)\) is the cardinality of a minimum forcing subset of S. The forcing total edge-to-vertex monophonic number of G, denoted by \(f_{tev}(G) = \textit{min}\{f_{tev}(S)\}\), where the minimum is taken over all total edge-to-vertex monophonic set S in G. The forcing total edge-to-vertex monophonic number of certain classes of graphs are determined and some of its general properties are studied. It is shown that for every integers a and b with \(0 \le a \le b\) and \(b \ge 2\), there exists a connected graph G such that \(f_{tev}(G) = a\) and \( m _{tev}(G) = b\), where \( f _{tev}(G)\) is the forcing total edge-to-vertex monophonic number of G.     

Subset sum problems with digraph constraints

We introduce and study optimization problems which are related to the well-known Subset Sum problem. In each new problem, a node-weighted digraph is given and one has to select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints called digraph constraints and maximality need to be satisfied. The digraph constraint imposes that a node must belong to the solution if at least one of its predecessors is in the solution. An alternative of this constraint says that a node must belong to the solution if all its predecessors are in the solution. The maximality constraint ensures that no superset of a feasible solution is also feasible. The combination of these constraints provides four problems. We study their complexity and present some approximation results according to the type of input digraph, such as directed acyclic graphs and oriented trees.     

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.     

New bounds for locally irregular chromatic index of bipartite and subcubic graphs

A graph is locally irregular if the neighbors of every vertex v have degrees distinct from the degree of v. A locally irregular edge-coloring of a graph G is an (improper) edge-coloring such that the graph induced on the edges of any color class is locally irregular. It is conjectured that three colors suffice for a locally irregular edge-coloring. In the paper, we develop a method using which we prove four colors are enough for a locally irregular edge-coloring of any subcubic graph admiting such a coloring. We believe that our method can be further extended to prove the tight bound of three colors for such graphs. Furthermore, using a combination of existing results, we present an improvement of the bounds for bipartite graphs and general graphs, setting the best upper bounds to 7 and 220, respectively.     

Contract design and insurance fraud: an experimental investigation

This paper experimentally examines the impact of contract design on insurance fraud. We test how fraud behavior varies for insurance contracts with full coverage, a straight deductible or claim-dependent premiums (bonus-malus contracts), in a setup where rational and selfish individuals have an incentive to always claim the maximum possible indemnity. We find a substantial impact of contractual arrangements: Deductible contracts lead to a greater extent to claim build-up than full coverage contracts. In contrast, bonus-malus contracts that entail the same net gains from fraud as deductible contracts do not increase claim build-up. Thus, our results indicate that bonus-malus contracts may be superior to deductible contracts for behavioral reasons.     

Probabilistic population projections for countries with generalized HIV/AIDS epidemics

In 2015, the United Nations (UN) issued probabilistic population projections for all countries up to 2100, by simulating future levels of total fertility and life expectancy and combining the results using a standard cohort component projection method. For the 40 countries with generalized HIV/AIDS epidemics, the mortality projections used the Spectrum/Estimation and Projection Package (EPP) model, a complex, multistate model designed for short-term projections of policy-relevant quantities for the epidemic. We propose a simpler approach that is more compatible with existing UN projection methods for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression and then converted to age- and sex-specific mortality rates using model life tables designed for countries with HIV/AIDS epidemics. These are then input to the cohort component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar short-run projections to Spectrum/EPP, while being simpler and avoiding multistate modelling.     

Cohort Differences in Parental Financial Help to Adult Children

In this article, we examine birth cohort differences in parents’ provision of monetary help to adult children with particular focus on the extent to which cohort differences in family structure and the transition to adulthood influence these changes. Using data from the Health and Retirement Study from 1994 to 2010, we compare financial help to children of three respondent cohorts as the parents in these birth cohorts from ages 53–58 to 57–62. We find that transfers to children have increased among more recent cohorts. Two trends—declining family size and children’s delay in marriage—account for part of the increase across cohorts. However, other trends, such as the increase in the number of stepchildren and increasing child’s income level, tend to decrease the observed cohort trend.     

Changing land tenure patterns in Scotland: A time for reform?

Land tenure patterns throughout Britain have changed significantly. The popularity of the traditional agricultural tenancy has declined and in response to legislative and policy developments landowners have become reluctant to enter into long-term tenancy arangements with tenants. The result has been a growth in a number of short term leases. In response, legislative reform took place in England and Wales during 1995 and introduced a farm business tenancy. It provides for greater freedom to negotiate individual agreements. However, Scotland has been excluded. This paper illustrates that Scotland has experienced similar changes to those observed elsewhere and that the main short term lease (limited partnership tenancy) currently popular with Scottish landowners is fraught with legal and administrative difficulties. The limited partnership tenancy is not a suitable alternative to the traditional agricultural tenancy and as such there may be a case for the extension of the farm business tenancy to Scotland.     

Exercise self-regulation among older women participating in a heart disease-management intervention

Using behavioral self-regulation processes may facilitate exercise among older women with heart disease. Data from women in a heart disease-management program (n = 658, mean 73 years), was used to explore associations among exercise self-regulation components (i.e., choosing to improve exercise and observing, judging, and reacting to one's behavior) and exercise capacity. General linear models showed that choosing exercise predicted higher exercise self-regulation scores postprogram and 8 months later. In turn, these scores predicted greater improvements in exercise capacity concurrently and 8 months later. Interaction analyses revealed that the effect of self-regulation on exercise capacity was stronger among women who chose to work on exercise.     

Research-in-Progress Sessions Create a More Inclusive and Engaging Regional Conference

The Pacific Sociological Association annual meeting recently added a new session type called the Research-in-Progress (RIP) session. The purpose of adding these sessions was to provide an opportunity for attendees to present research still in formative stages of completion in order to get useful feedback. Presentations ranged from doctoral dissertation proposals to nearly completed research. Early experience from RIP session organizers and discussants is that these sessions were lively and engaging, sparking a great deal of audience participation. Feedback from presenters indicated that they received useful feedback. Based on our initial experience with the RIP sessions, we believe they are a beneficial addition to the meetings.