Problems on Shortest k-Node Cycles and Paths

The paper is devoted to the construction of mathematical models for problems on the shortest cycles and paths, that pass through a given number of nodes of a directed graph. Such cycles and paths are called k-node, where 1<k <n, n is the number of nodes in the graph. Section 1 formulates two problems for finding the shortest k-node cycle – a mixed Boolean and linear programming problem and a discrete programming problem. Both problems include constraints from the classical assignment problem, describing a one-time entry into a node and a one-time exit from a node for those nodes through which the cycle passes. The cycle connectivity in the first problem is ensured by modeling the flow problem, and in the second problem, it is ensured by using the A. Tucker constraints for the travelling salesman problem. Section 2 establishes a connection between the formulations of both problems from Section 1 and the travelling salesman problem and investigates the efficiency of their solution using modern versions of gurobi and cplex programs and the AMPL modeling language. Section 3 contains the formulation of the shortest k-node path problem, which is represented by a mixed Boolean and linear programming problem. With its help, the optimal routes were found for visiting the wine-making points of the Malopolskie Wine Route in the direction Lviv-Wroclaw-Lviv (Section 4). Here a map for the 20 most visited wine-making points of the Malopolskie Wine Route and a table of the distances between them and the distances from them to Lviv and Wroclaw, calculated using the Google Maps web service, are presented. The developed mathematical models of the problems of finding the shortest k-node paths and cycles and the developed software in the AMPL modeling language can be used for the design and arrangement of technical objects, optimization of the transportation of products, analysis and forecasting of economic processes, determination of optimal routes when planning passenger and freight traffic, optimal organization of the process of managing a set of transactions and queries during their implementation in network databases and other classes of applied optimization problems. Keywords: digraph, shortest path, Boolean variable, linear programming, Hamiltonian cycle, Hamiltonian path, travelling salesman problem, AMPL, gurobi, cplex.

P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53

In this paper, we consider P53-Mdm2 negative feedback loop supposed to be the core circuit of genome. We study stability and the oscillatory dynamics of the loop. Many of the studies modeled this loop by delay-differential equations with P53-induced transcrip- tional delay in the production of Mdm2. We, however, highlight the importance of Mdm2- induced delay in the degradation of P53 protein. We consider two forms of P53 protein i.e., plain P53 and active P53 along with its principal antagonist protein Mdm2 to formulate a minimal model. Active P53 finds its inclusion in the loop in the presence of DNA damage represented by a Boolean variable ‘s’. The analysis of the model provides thresholds on delays using Nyquist criterion such that delays in the degradation of P53 lower than these thresholds guarantee stability of the loop in that all proteins plain P53, active P53 and Mdm2 approach to stable equilibrium state. The oscillatory dynamics in proteins, if any, would exist beyond these thresholds.

On the Issue of Identification of Urgent Instruments of Anti-Crisis Management of Enterprises

The article examines the urgent anti-crisis management instruments that characterize immediate (urgent) actions aimed at eliminating or reducing the negative impact of crisis phenomena on the enterprise. For the purpose of their identification, carrying out a comparative analysis is recommended, on the basis of the indicators that provide for assessment according to the following criteria: implementation time (time of accomplishing of operations for implementation of the anti-crisis control instrument, time of one operation for implementation of the anti-crisis management instrument, the level of time for operations for implementation of the anti-crisis management instrument); riskiness (coefficient of possible loss of profitability, Altman’s Z-criterion, indicator of financial sustainability of the enterprise); level of competitiveness (product competitiveness index, assessment of the competitiveness of the enterprise in statistics, multi-factory model of competitiveness); profitability of the enterprise (net profit per 1 UAH of costs for implementation of the anti-crisis management instrument, profitability of products, the level of costs for implementation of the anti-crisis management instrument). In the process of identification of the anti-crisis management instruments, the aggregate of the obtained indicators was carried out according to the results of compliance with the established criterion value using Boolean variables. A scale of values is formed; it is determined that the enterprise’s considering the anti-crisis management instrument as the urgent one should take place on the basis of satisfaction of more than 65% of the signs of compliance with the standards for the indicators expressed in the value of the boolean variable. In the process of practical approbation of the recommended method, the urgent instruments for the anti-crisis management of PJSC «Kontsern Khlibprom» are identified.

Nonlinear Characteristics of Semiconductor Optical Amplifiers for Optical Switching Control Realization of Logic Gates

This paper studies the problem of data access at the receiver with large bit error rate and low quality factor. Due to this issue the information got inaccurately at the receiver side, the data should have high quality factor and low bit error rate to be simple of identification at the receiver when using the gates. The nonlinear properties of the semiconductor optical amplifier are utilized to accomplish the Boolean variable based math work, in which AND, NAND, and OR gates potentially used to endorse the Boolean function. Through blend this gates together any Boolean function can be accomplished and utilized to perform optical signal processing. The quality factor and BER are measured by utilizing the eye diagram analyzer, the state of the output bit and also shaped by the oscilloscope visualizer in optiwave simulation program. These models can be used for wavelength converter, header recognition, parity checking, binary addition, packet-header modification, encoding and encryption with pattern matching, and data encryption with high speed and high quality factor.

MAX-SAT Problem using Hybrid Harmony Search Algorithm

Maximum Satisfiability problem is an optimization variant of the Satisfiability problem (SAT) denoted as MAX-SAT. The aim of this problem is to find Boolean variable assignment that maximizes the number of satisfied clauses in the Boolean formula. In case the number of variables per clause is equal or greater than three, then this problem is considered NP-complete. Hence, many researchers have developed techniques to deal with MAX-SAT. In this paper, we investigate the impact of different hybrid versions of binary harmony search (HS) algorithm on solving MAX 3-SAT problem. Therefore, we propose two novel hybrid binary HS algorithms. The first hybridizes Flip heuristic with HS, and the second uses Tabu search combined with Flip heuristic. Furthermore, a distinguished feature of our proposed approaches is using an objective function that is updated dynamically based on the stepwise adaptation of weights (SAW) mechanism to evaluate the MAX-SAT solution using the proposed hybrid versions. The performance of the proposed approaches is evaluated over standard MAX-SAT benchmarks, and the results are compared with six evolutionary algorithms and three stochastic local search algorithms. The obtained results are competitive and show that the proposed novel approaches are effective.

Annual variation in event-scale precipitation <i>δ</i>²H at Barrow, AK, reflects vapor source region

In this study, precipitation isotopic variations at Barrow, AK, USA, are linked to conditions at the moisture source region, along the transport path, and at the precipitation site. Seventy precipitation events between January 2009 and March 2013 were analyzed for δ2H and deuterium excess. For each precipitation event, vapor source regions were identified with the hybrid single-particle Lagrangian integrated trajectory (HYSPLIT) air parcel tracking program in back-cast mode. The results show that the vapor source region migrated annually, with the most distal (proximal) and southerly (northerly) vapor source regions occurring during the winter (summer). This may be related to equatorial expansion and poleward contraction of the polar circulation cell and the extent of Arctic sea ice cover. Annual cycles of vapor source region latitude and δ2H in precipitation were in phase; depleted (enriched) δ2H values were associated with winter (summer) and distal (proximal) vapor source regions. Precipitation δ2H responded to variation in vapor source region as reflected by significant correlations between δ2H with the following three parameters: (1) total cooling between lifted condensation level (LCL) and precipitating cloud at Barrow, ΔTcool, (2) meteorological conditions at the evaporation site quantified by 2 m dew point, Td, and (3) whether the vapor transport path crossed the Brooks and/or Alaskan ranges, expressed as a Boolean variable, mtn. These three variables explained 54 % of the variance (p<0. 001) in precipitation δ2H with a sensitivity of −3.51 ± 0.55 ‰ °C−1 (p<0. 001) to ΔTcool, 3.23 ± 0.83 ‰ °C−1 (p<0. 001) to Td, and −32.11 ± 11.04 ‰ (p = 0. 0049) depletion when mtn is true. The magnitude of each effect on isotopic composition also varied with vapor source region proximity. For storms with proximal vapor source regions (where ΔTcool <7 °C), ΔTcool explained 3 % of the variance in δ2H, Td alone accounted for 43 %, while mtn explained 2 %. For storms with distal vapor sources (ΔTcool > 7°C), ΔTcool explained 22 %, Td explained only 1 %, and mtn explained 18 %. The deuterium excess annual cycle lagged by 2–3 months during the δ2H cycle, so the direct correlation between the two variables is weak. Vapor source region relative humidity with respect to the sea surface temperature, hss, explained 34 % of variance in deuterium excess, (−0.395 ± 0.067 ‰ %−1, p<0. 001). The patterns in our data suggest that on an annual scale, isotopic ratios of precipitation at Barrow may respond to changes in the southerly extent of the polar circulation cell, a relationship that may be applicable to interpretation of long-term climate change records like ice cores.

Annual variation in precipitation δ²H reflects vapor source region at Barrow, AK

Interpretation of variability in precipitation stable isotopic ratios often relies exclusively on empirical relationships to meteorological variables (e.g., temperature) at the precipitation site. Because of the difficulty of unambiguously determining the vapor source region(s), relatively fewer studies consider evaporation and transport conditions. Increasing accessibility of Lagrangian air parcel tracking programs now allows for an integrated look at the relationship between the precipitation isotope ratios and the evolution of moist air masses. In this study, 70 precipitation events occurring between January 2009 and March 2013 at Barrow, AK, USA, were analyzed for δ2H and deuterium excess. For each precipitation event, vapor source regions were identified with the Lagrangian air parcel tracking program, HYSPLIT, in back-cast mode. The results show that the vapor source region migrated annually with the most distal (proximal) and southerly (northerly) vapor source regions occurred during the winter (summer). This may be linked to equatorial expansion and poleward contraction of the Polar circulation cell and the extent of Arctic sea ice cover. Annual cycles of vapor source region latitude and δ2H in precipitation were in phase; depleted (enriched) δ2H values were associated with winter (summer) and distal (proximal) vapor source regions. Precipitation δ2H responded to variation in vapor source region as reflected by significant correlations between δ2H with the following three parameters: 1) total cooling between lifted condensation level and precipitating cloud at Barrow, ΔTcool, 2) the meteorological conditions at the evaporation site quantified by 2 m dew point, Td, and 3) whether the transport crossed the Brooks and/or Alaskan ranges, expressed as a Boolean variable, mtn. These three variables explained 52 % of the variance (p