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.

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

2010 Mathematics Subject Classification: 60J80.

Analysis of purchasing activity with discounted cash flow inventory models = Beszerzési tevékenység elemzése diszkontált pénzáramlású készletmodellel

A klasszikus tételnagyság probléma két fontosabb készletezési költséget ragad meg: rendelési és készlettartási költségek. Ebben a dolgozatban a vállalatok készpénz áramlásának a beszerzési tevékenységre gyakorolt hatását vizsgáljuk. Ebben az elemzésben a készpénzáramlási egyenlőséget használjuk, amely nagyban emlékeztet a készletegyenletekre. Eljárásunkban a beszerzési és rendelési folyamatot diszkontálva vizsgáljuk. A költségfüggvény lineáris készpénztartási, a pénzkiadás haszonlehetőség és lineáris kamatköltségből áll. Bemutatjuk a vizsgált modell optimális megoldását. Az optimális megoldást egy számpéldával illusztráljuk. = The classical economic order quantity model has two types of costs: ordering and inventory holding costs. In this paper we try to investigate the effect of purchasing activity on cash flow of a firm. In the examinations we use a cash flow identity similar to that of in inventory modeling. In our approach we analyze the purchasing and ordering process with discounted costs. The cost function of the model consists of linear cash holding, linear opportunity cost of spending cash, and linear interest costs. We show the optimal solution of the proposed model. The optimal solutions will be presented by numerical examples.

Perturbative discrete-time multivariate fiber channel model with finite memory

We introduce a discrete-time fibre channel model that provides an accurate analytical description of signal-signal and signal-noise interference with memory defined by the interplay of nonlinearity and dispersion. Also the conditional pdf of signal distortion, which captures non-circular complex multivariate symbol interactions, is derived providing the necessary platform for the analysis of channel statistics and capacity estimations in fibre optic links.

Noise resilient discrete-time cross-relation sensor characterisation

In-situ characterisation of thermocouple sensors is a challenging problem. Recently the authors presented a blind characterisation technique based on the cross-relation method of blind identification. The method allows in-situ identification of two thermocouple probes, each with a different dynamic response, using only sampled sensor measurement data. While the technique offers certain advantages over alternative methods, including low estimation variance and the ability to compensate for noise induced bias, the robustness of the method is limited by the multimodal nature of the cost function. In this paper, a normalisation term is proposed which improves the convexity of
the cost function. Further, a normalisation and bias compensation hybrid approach is presented that exploits the advantages of both normalisation and bias compensation. It is found that the optimum of the hybrid cost function is less biased and more stable than when only normalisation is applied. All results were verified by simulation.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

On Reasonable Space and Time Cost Models for the λ-Calculus

Slot and van Emde Boas Invariance Thesis states that a time (respectively, space) cost model is reasonable for a computational model C if there are mutual simulations between Turing machines and C such that the overhead is polynomial in time (respectively, linear in space). The rationale is that under the Invariance Thesis, complexity classes such as LOGSPACE, P, PSPACE, become robust, i.e. machine independent. In this dissertation, we want to find out if it possible to define a reasonable space cost model for the lambda-calculus, the paradigmatic model for functional programming languages. We start by considering an unusual evaluation mechanism for the lambda-calculus, based on Girard's Geometry of Interaction, that was conjectured to be the key ingredient to obtain a space reasonable cost model. By a fine complexity analysis of this schema, based on new variants of non-idempotent intersection types, we disprove this conjecture. Then, we change the target of our analysis. We consider a variant over Krivine's abstract machine, a standard evaluation mechanism for the call-by-name lambda-calculus, optimized for space complexity, and implemented without any pointer. A fine analysis of the execution of (a refined version of) the encoding of Turing machines into the lambda-calculus allows us to conclude that the space consumed by this machine is indeed a reasonable space cost model. In particular, for the first time we are able to measure also sub-linear space complexities. Moreover, we transfer this result to the call-by-value case. Finally, we provide also an intersection type system that characterizes compositionally this new reasonable space measure. This is done through a minimal, yet non trivial, modification of the original de Carvalho type system.

Characteristic study, its identification and self-tuned approach to control hydro-power plants

The water time constant and mechanical time constant greatly influences the power and speed oscillations of hydro-turbine-generator unit. This paper discusses the turbine power transients in response to different nature and changes in the gate position. The work presented here analyses the characteristics of hydraulic system with an emphasis on changes in the above time constants. The simulation study is based on mathematical first-, second-, third- and fourth-order transfer function models. The study is further extended to identify discrete time-domain models and their characteristic representation without noise and with noise content of 10 & 20 dB signal-to-noise ratio (SNR). The use of self-tuned control approach in minimising the speed deviation under plant parameter changes and disturbances is also discussed.

Analyzing change in medication use - statistical approaches

The objective of this study was to gain an understanding of the effects of population heterogeneity, missing data, and causal relationships on parameter estimates from statistical models when analyzing change in medication use. From a public health perspective, two timely topics were addressed: the use and effects of statins in populations in primary prevention of cardiovascular disease and polypharmacy in older population. Growth mixture models were applied to characterize the accumulation of cardiovascular and diabetes medications among apparently healthy population of statin initiators. The causal effect of statin adherence on the incidence of acute cardiovascular events was estimated using marginal structural models in comparison with discrete-time hazards models. The impact of missing data on the growth estimates of evolution of polypharmacy was examined comparing statistical models under different assumptions for missing data mechanism. The data came from Finnish administrative registers and from the population-based Geriatric Multidisciplinary Strategy for the Good Care of the Elderly study conducted in Kuopio, Finland, during 2004–07. Five distinct patterns of accumulating medications emerged among the population of apparently healthy statin initiators during two years after statin initiation. Proper accounting for time-varying dependencies between adherence to statins and confounders using marginal structural models produced comparable estimation results with those from a discrete-time hazards model. Missing data mechanism was shown to be a key component when estimating the evolution of polypharmacy among older persons. In conclusion, population heterogeneity, missing data and causal relationships are important aspects in longitudinal studies that associate with the study question and should be critically assessed when performing statistical analyses. Analyses should be supplemented with sensitivity analyses towards model assumptions.

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Swapping space for time and unfair tests of ecological models

Testing ecological models for management is an increasingly important part of the maturation of ecology as an applied science. Consequently, we need to work at applying fair tests of models with adequate data. We demonstrate that a recent test of a discrete time, stochastic model was biased towards falsifying the predictions. If the model was a perfect description of reality, the test falsified the predictions 84% of the time. We introduce an alternative testing procedure for stochastic models, and show that it falsifies the predictions only 5% of the time when the model is a perfect description of reality. The example is used as a point of departure to discuss some of the philosophical aspects of model testing.

Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010