Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Characterizing graph symmetries through quantum Jensen-Shannon divergence

In this paper we investigate the connection between quantum walks and graph symmetries. We begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse. To achieve this, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the quantum Jensen-Shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries. Hence, we assign to each pair of nodes of the graph a value of the divergence, and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph. © 2013 American Physical Society.

Approximate axial symmetries from continuous time quantum walks

The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk which is evolved through time. By measuring the probability that the quantum walker to visits each node of the network in this time frame, we are able to determine whether the two vertices are symmetrical with respect to any axis of the graph. Moreover, we show that we are able to successfully detect approximate axial symmetries too. We show the efficacy of our approach by analysing both synthetic and real-world data. © 2012 Springer-Verlag Berlin Heidelberg.

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Implementing an agent-based model with a spatial visual display in discrete-event simulation software

There has been an increasing interest in the use of agent-based simulation and some discussion of the relative merits of this approach as compared to discrete-event simulation. There are differing views on whether an agent-based simulation offers capabilities that discrete-event cannot provide or whether all agent-based applications can at least in theory be undertaken using a discrete-event approach. This paper presents a simple agent-based NetLogo model and corresponding discrete-event versions implemented in the widely used ARENA software. The two versions of the discrete-event model presented use a traditional process flow approach normally adopted in discrete-event simulation software and also an agent-based approach to the model build. In addition a real-time spatial visual display facility is provided using a spreadsheet platform controlled by VBA code embedded within the ARENA model. Initial findings from this investigation are that discrete-event simulation can indeed be used to implement agent-based models and with suitable integration elements such as VBA provide the spatial displays associated with agent-based software.

Using discrete event simulation to investigate road delivery policies to UK retailers

Retail customers provide a number of significant challenges to the efficiency and effectiveness of distribution systems. These challengers include shorter delivery windows, fluctuating volumes and a wider product mix. This paper demonstrates the use of discrete-event simulation to investigate policy issues regarding the incorporation of retail customers in a road delivery network from the spoke terminal of a hub and spoke distribution system. In particular a comparison of a mixed (retail and non-retail) delivery policy with a dedicated retail delivery run is made.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

A diszkrét kiválasztási modell becslése Cox-regresszióval (Parameter estimation for multinomial discrete choice model using Cox-regression)

Considering the so-called "multinomial discrete choice" model the focus of this paper is on the estimation problem of the parameters. Especially, the basic question arises how to carry out the point and interval estimation of the parameters when the model is mixed i.e. includes both individual and choice-specific explanatory variables while a standard MDC computer program is not available for use. The basic idea behind the solution is the use of the Cox-proportional hazards method of survival analysis which is available in any standard statistical package and provided a data structure satisfying certain special requirements it yields the MDC solutions desired. The paper describes the features of the data set to be analysed.

Lie-szimmetriák egy közgazdasági alkalmazása (An economic application of the Lie symmetries)

Ebben a tanulmányban ismertetjük a Nöther-tétel lényegi vonatkozásait, és kitérünk a Lie-szimmetriák értelmezésére abból a célból, hogy közgazdasági folyamatokra is alkalmazzuk a Lagrange-formalizmuson nyugvó elméletet. A Lie-szimmetriák dinamikai rendszerekre történő feltárása és viselkedésük jellemzése a legújabb kutatások eredményei e területen. Például Sen és Tabor (1990), Edward Lorenz (1963), a komplex kaotikus dinamika vizsgálatában jelent®s szerepet betöltő 3D modelljét, Baumann és Freyberger (1992) a két-dimenziós Lotka-Volterra dinamikai rendszert, és végül Almeida és Moreira (1992) a három-hullám interakciós problémáját vizsgálták a megfelelő Lie-szimmetriák segítségével. Mi most empirikus elemzésre egy közgazdasági dinamikai rendszert választottunk, nevezetesen Goodwin (1967) ciklusmodelljét. Ennek vizsgálatát tűztük ki célul a leírandó rendszer Lie-szimmetriáinak meghatározásán keresztül. / === / The dynamic behavior of a physical system can be frequently described very concisely by the least action principle. In the centre of its mathematical presentation is a specic function of coordinates and velocities, i.e., the Lagrangian. If the integral of the Lagrangian is stationary, then the system is moving along an extremal path through the phase space, and vice versa. It can be seen, that each Lie symmetry of a Lagrangian in general corresponds to a conserved quantity, and the conservation principle is explained by a variational symmetry related to a dynamic or geometrical symmetry. Briey, that is the meaning of Noether's theorem. This paper scrutinizes the substantial characteristics of Noether's theorem, interprets the Lie symmetries by PDE system and calculates the generators (symmetry vectors) on R. H. Goodwin's cyclical economic growth model. At first it will be shown that the Goodwin model also has a Lagrangian structure, therefore Noether's theorem can also be applied here. Then it is proved that the cyclical moving in his model derives from its Lie symmetries, i.e., its dynamic symmetry. All these proofs are based on the investigations of the less complicated Lotka Volterra model and those are extended to Goodwin model, since both models are one-to-one maps of each other. The main achievement of this paper is the following: Noether's theorem is also playing a crucial role in the mechanics of Goodwin model. It also means, that its cyclical moving is optimal. Generalizing this result, we can assert, that all dynamic systems' solutions described by first order nonlinear ODE system are optimal by the least action principle, if they have a Lagrangian.

Preferences of Hungarian consumers for quality, access and price attributes of health care services — result of a discrete choice experiment

In 2010, a household survey was carried out in Hungary among 1037 respondents to study consumer preferences and willingness to pay for health care services. In this paper, we use the data from the discrete choice experiments included in the survey, to elicit the preferences of health care consumers about the choice of health care providers. Regression analysis is used to estimate the effect of the improvement of service attributes (quality, access, and price) on patients’ choice, as well as the differences among the socio-demographic groups. We also estimate the marginal willingness to pay for the improvement in attribute levels by calculating marginal rates of substitution. The results show that respondents from a village or the capital, with low education and bad health status are more driven by the changes in the price attribute when choosing between health care providers. Respondents value the good skills and reputation of the physician and the attitude of the personnel most, followed by modern equipment and maintenance of the office/hospital. Access attributes (travelling and waiting time) are less important. The method of discrete choice experiment is useful to reveal patients’ preferences, and might support the development of an evidence-based and sustainable health policy on patient payments.

Trading between perceived risks and benefits related to biosimilar biological treatment in Crohn’s disease; discrete choice experiment among gastroenterologists

Objective: The objective of the study is to explore preferences of gastroenterologists for biosimilar drugs in Crohn’s Disease and reveal trade-offs between the perceived risks and benefits related to biosimilar drugs. Method: Discrete choice experiment was carried out involving 51 Hungarian gastroenterologists in May, 2014. The following attributes were used to describe hypothetical choice sets: 1) type of the treatment (biosimilar/originator) 2) severity of disease 3) availability of continuous medicine supply 4) frequency of the efficacy check-ups. Multinomial logit model was used to differentiate between three attitude types: 1) always opting for the originator 2) willing to consider biosimilar for biological-naïve patients only 3) willing to consider biosimilar treatment for both types of patients. Conditional logit model was used to estimate the probabilities of choosing a given profile. Results: Men, senior consultants, working in IBD center and treating more patients are more likely to willing to consider biosimilar for biological-naïve patients only. Treatment type (originator/biosimilar) was the most important determinant of choice for patients already treated with biologicals, and the availability of continuous medicine supply in the case biological-naïve patients. The probabilities of choosing the biosimilar with all the benefits offered over the originator under current reimbursement conditions are 89% vs 11% for new patients, and 44% vs 56% for patients already treated with biological. Conclusions: Gastroenterologists were willing to trade between perceived risks and benefits of biosimilars. The continuous medical supply would be one of the major benefits of biosimilars. However, benefits offered in the scenarios do not compensate for the change from the originator to the biosimilar treatment of patients already treated with biologicals.