General gauge-Yukawa-quartic β-functions at 4-3-2-loop order

We determine the full set of coefficients for the completely general 4-loop gauge and 3-loop Yukawa β-functions for the most general renormalizable four-dimensional theories. Using a complete parametrization of the β-functions, we compare the general form to the specific β-functions of known theories to constrain the unknown coefficients. The Weyl consistency conditions provide additional constraints, completing the determination.

The knapsack problem with special neighbor constraints

The knapsack problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two knapsack problems which contain additional constraints in the form of directed graphs whose vertex set corresponds to the item set. In the one-neighbor knapsack problem, an item can be chosen only if at least one of its neighbors is chosen. In the all-neighbors knapsack problem, an item can be chosen only if all its neighbors are chosen. For both problems, we consider uniform and general profits and weights. We prove upper bounds for the time complexity of these problems when restricting the graph constraints to special sets of digraphs. We discuss directed co-graphs, minimal series-parallel digraphs, and directed trees.

An approach to finding a global optimum in constrained clustering tasks involving the assessments of several experts

An approach to solving the constrained clustering problem has been developed, based on the aggregation of data obtained as a result of evaluating the characteristics of clustered objects by several independent experts, and the analysis of alternative variants of clustering by constraint programming methods using original heuristics. Objects clusterized are represented as multisets, which makes it possible to use appropriate methods of aggregation of expert opinions. It is proposed to solve the constrained clustering problem as a constraint satisfaction problem. The main attention is paid to the issue of reducing the number and simplifying the constraints of the constraint satisfaction problem at the stage of its formalization. Within the framework of the approach, we have created: a) a method for estimating the optimal value of the objective function by hierarchical clustering of multisets, taking into account a priori constraints of the subject domain, and b) a method for generating additional constraints on the desired solution in the form of “smart tables”, based on the obtained estimate. The approach allows us to find the best partition in the problems of the class under consideration, which are characterized by a high dimension.

Equivalent cyclic polygon of a euclidean travelling salesman problem tour and modified formulation

We define a geometric transformation of Euclidean Travelling Salesman Problem (TSP) tours that leads to a new formulation of the TSP. For every Euclidean TSP n-city tour, it is possible to construct an inscribed n-polygon (Equivalent Cyclic Polygon, ECP) such that the lengths of the edges are equal to the corresponding TSP tour links and follow the same sequence order. The analysis of the ECP elicits the possibility of defining a new objective function in terms of angles instead of distances. This modification opens the way to identify characterizing geometric parameters of the TSP as well as to explore new heuristics based on the inclusion of additional constraints. The experimentation with a set of cases shows promising results compared to the traditional compact formulations. The behavior of the ECP-based TSP formulations is better when the nodes of the TSP are randomly or evenly distributed.

How do Cl concentrations matter for simulating CH₄, δ¹³C(CH₄) and estimating CH₄ budget through atmospheric inversions?

Atmospheric methane (CH4) concentrations have been rising since 2007, resulting from an imbalance between CH4 sources and sinks. The CH4 budget is generally estimated through top-down approaches using CH4 observations as constraints. The atmospheric isotopic CH4 signal, δ13C(CH4), can also provide additional constraints and helps to discriminate between emission categories. The oxidation by chlorine (Cl) likely contributes less than 5 % to the total oxidation of atmospheric CH4. However, the Cl sink is highly fractionating, and thus strongly influences δ13C(CH4). As inversion studies do not prescribe the same Cl fields to constrain CH4 budget, it can lead to discrepancies between estimates. To quantify the influence of the Cl concentrations on CH4, δ13C(CH4) and CH4 budget estimates, we perform multiple sensitivity simulations using three Cl fields with concentrations that are realistic with regard to recent literature and one Cl field with concentrations that are very likely to be overestimated. We also test removing the tropospheric and the entire Cl sink in other sensitivity simulations. We find that the realistic Cl fields tested here are responsible for between 0.3 % and 1.8 % of the total chemical CH4 sink in the troposphere and between 1.0 % and 1.2 % in the stratosphere. Prescribing these different Cl amounts in surface-based inversions can lead to differences in global CH4 source adjustments of up to 12.3 TgCH4.yr−1. We also find that the globally-averaged isotopic signature of the CH4 sources inferred by a surface-based inversion assimilating δ13C(CH4) observations would decrease by 0.53 ‰ for each additional percent of contribution from the tropospheric Cl sink to the total sink. Finally, our study shows that CH4 seasonal cycle amplitude is modified by less than 1–2 % but δ13(CH4) seasonal cycle amplitude can be modified by up to 10–20 %, depending on the latitude.

Hiring schedule optimization at the Surrey fire department

PurposeThe Surrey (British Columbia, Canada) fire department has an annual cycle for hiring full-time firefighters. This paper optimizes the timing of the annual hiring period. A key issue is handling workplace absences, which can be covered by overtime cost or full-time hires.Design/methodology/approachShort-term and long-term absences patterns are analyzed according to season and age cohorts of the firefighters. These are then used in both an explanatory and time series model to predict future absences. The hiring schedule is optimized based on these predictions and additional constraints.FindingsThe current practice fares well in the analysis. For the time period studied, moving to earlier hiring dates appears beneficial. This analysis is robust with respect to various assumptions.Originality/valueThis is a case study where analytic techniques and machine learning are applied to an organizational practice that is not commonly analyzed. In this case, the previous method was not much worse than the optimized solution. The techniques used are quite general and can be applied to various organizational decision problems.

Simplified group activity selection with group size constraints

Several real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.

A quantitative method for deriving salinity of subglacial water using ground-based transient electromagnetics

Liquid water can exist at temperatures well below freezing beneath glaciers and ice sheets, where subglacial water systems, fresh and saline, have been shown to host unique microbial ecosystems. Geophysical techniques sensitive to fluid-content contrasts, e.g. electromagnetics, can characterize subglacial water and its salinity. Here, we assess the ground-based transient electromagnetic (TEM) method for deriving the resistivity and salinity of subglacial water. We adapt an existing open-source Bayesian inversion algorithm, which uses independent depth constraints, to output posterior distributions of resistivity and pore fluid salinity with depth. A variety of synthetic models, including a thin (5 m), conductive (0.16 Ωm), hypersaline (147 psu) subglacial lake, are used to evaluate the TEM method for imaging under 800 m-thick ice. The study demonstrates that TEM methods can resolve conductive, saline bodies accurately using external depth constraints, for example, from radar or seismic data. The depth resolution of TEM can be limited beneath deep (>800 m), thick (>50 m) conductive, water bodies and additional constraints from passive electromagnetic (EM) methods could be used to reduce ambiguities in the TEM results. Subsequently, non-invasive active and passive EM methods could provide profound insights into remote aqueous systems under glaciers and ice sheets.

Duality-invariant extensions of Einstein-Maxwell theory

We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the curvature. Then we explore the effect of field redefinitions and we show that, to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators. We conjecture that this is a general phenomenon at all orders, i.e., that any duality-invariant extension of Einstein-Maxwell theory is perturbatively equivalent to a higher-derivative gravity minimally coupled to Maxwell theory. Finally, we study charged black hole solutions in the six-derivative theory and we investigate additional constraints on the couplings motivated by the weak gravity conjecture.