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Solving a quantum few-body problem with weak interaction is a complicated task. A procedure for discrete variable representation is developed and applied, allowing the period of calculation to be reduced with no loss of accuracy.

A new formula expressing explicitly the integrals, antidifference, of discrete orthogonal polynomials $$\{P_{n}(x):$$ Hahn, Meixner, Kravchuk, and Charlier $$\}$$ of any degree in terms of $$P_{n}(x)$$ themselves are proved. Other formulae for the expansion coefficients of general-order difference integrations $$\nabla ^{-s}f(x),\,\Delta ^{-s}f(x),$$ $$\nabla ^{-s}[x^{\ell }\nabla ^{q}f(x)]\,$$ and $$\Delta ^{-s}[x^{\ell }\Delta ^{q}f(x)],$$ of an arbitrary function f(x) of a discrete variable in terms of its original expansion coefficients are also obtained. Application of these formulae for solving ordinary difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained.

Trabalho de Projeto do Mestrado em Engenharia Física apresentado à Faculdade de Ciências e Tecnologia São cada vez mais necessários desenvolvimentos em métodos de encriptação que permitam comunicação perfeitamente segura sobre a ameaça de qualquer entidade externa. Essa necessidade surge relacionada com a continua informatização dos dados de qualquer indivíduo.O desenvolvimento de um sistema de encriptação teoricamente infalível está limitado pelo problema de distribuição de chaves, que é passível de intrusão. Certas propriedades quânticas oferecem uma solução possível para a criação de um sistema robusto de distribuição de chaves para encriptação. Exploração de propriedades quânticas, como o principio da incerteza de Heisenberg ou o teorema da não clonagem, permitem a deteção de intrusão durante a distribuição de chaves, pelo efeito que têm no aumento de uma taxa de erro. No entanto, o sistema fica mais sensível e vulnerável a erros em comparação a outros sistemas de encriptação comummente utilizados. Este aumento em dificuldade leva a que o hardware necessário seja mais complexo. O aumento da complexidade do hardware, no entanto, não compensa, atualmente, as perdas em distância e frequência de encriptação. Devido a tal muito trabalho ainda tem de ser feito em otimização e compensação de erros.Esta dissertação foca-se na apresentação de um método de otimização de um transmissor num sistema distribuição de chaves de encriptação quânticas. Os bits quânticos nesta aplicação são codificados utilizando o estado de polarização de fotões. Este método de codificação é geralmente referido de, Distribuição de Chaves Quânticas com Variáveis Discretas (DV-QKD). O transmissor utiliza um Controlador de Polarização Elétrico (EPC) que modifica a estado de polarização da luz consoante a tensão elétrica aplicada aos vários estágios que o constituem. Nesta dissertação procuramos otimizar a escolha de tensões a aplicar ao controlador de polarização elétrico. O objetivo é obter os seis estados de polarização necessários à saída do EPC no menor intervalo de tensões possível. O processo de criação da função custo, escolha e aplicação de um algoritmo de machine learning é discutido detalhadamente. Embora não sabendo todas as caraterísticas do EPC, relacionadas com a calibração, resultados que validam os dados obtidos numericamente pelo algoritmo são demonstrados. A aplicação do algoritmo, Otimização de Enxame de Partículas (PSO), como método de otimização da geração dos estados de polarização, foi relizada com sucesso. Resultados obtidos provam que transições entre os seis estados de polarização, usados em sistemas distribuição de chaves quânticas, são possiveis num intervalo de tensão inferior a 10 V em cada pino de controlo de um estágio do EPC, um valor pequeno quando comparado à gama de total de 140 V do EPC utilizado.A hipótese de utilizar outra versão deste algoritmo como método de compensação a desvios, em relação ao estado de polarização esperado, é também discutido. Development of encryption methods that allow for perfectly secure communications under threat of any external entity are increasingly needed with continuously informatization of data from any person. The development of an encryption system infallible in theory is limited by the a key distribution problem. Certain quantum properties offer a possible solution in the creation of a robust system for distribution of encryption keys.The exploitation of quantum properties, like Heisenberg's uncertainty principle or the non cloning theorem, allow for intruder detection during key distribution, due to the error rate increment introduced. However this makes the overall system much more sensible and prone to errors, when compared to the most commonly used encryption methods. This increased difficulty makes it so the hardware necessary is much more complex. This increment in complexity does not yet compensate for loses in distance and communication speeds when compared to other commonly used non quantum encryption methods. Due to that a lot of work still needs to be done in optimization and error compensation.This dissertation focuses in the presentation of a method to optimize a quantum key distribution transmitter. The quantum bits utilized in this application are codified in the polarization state of photons. This encryption method is commonly referred as Discrete Value Quantum Key Distribution (DV-QKD). The transmitter employs a Electrical Polarization Controller (EPC) that modifies light state of polarization according to the voltage applied to several stages comprising the device. In this dissertation we look to optimize the voltage choices that we will apply to the EPC. The goal is to obtain every required state of polarization at it's output in lowest voltage interval between each state possible.The creation process of the cost function, the choice and application of a machine learning algorithm is discussed in detail. Even though we don't know every characteristic of the EPC, related to it's calibration, results that validate the data obtained numerically by the algorithm are presented.The application of the algorithm, Particle Swarm Optimization (PSO), as a method to optimize the generation of polarization states, was done successfully. Results show that transitions between six states of polarization used in QKD systems can be generated using a voltagerange of 10 V for each stage controlling pin, a small value when compared to the standard full range of the drive voltages, which in the employed EPC equals 140 V.The hypothesis of using a variation of this algorithm as a method to compensate deviations, in relation to the expected state of polarization, is also discussed. Outro - Este trabalho é financiado pelo Fundo Europeu de Desenvolvimento Regional (FEDER), através do Programa Operacional Competitividade e Internacionalização (COMPETE 2020) do Portugal 2020 [Projeto Q.DOT com o nº 039728 (POCI-01-0247-FEDER-039728)]

This paper presents a new computational procedure for optimization of structures subjected to dynamic loads. The optimization problem is formulated with discrete design variables that represent the members from a table of commercially available members. Also, the requirements in the American Institute of Steel Construction (AISC) manual are formulated as constraints. This results in a nondifferentiable optimization problem. In the new procedure, the dynamic load is transformed into equivalent static loads (ESLs). Then the static response optimization problem having discrete design variables is solved using a metaheuristic optimization algorithm. Three methods to calculate the ESLs are investigated. It is found that the ESL cycles cannot converge to the final design. Therefore after a few ESL cycles, the original dynamic loads need to be used in the optimization process. Four example problems are solved to analyze the procedure. Based on this analysis, it is concluded that the new procedure is more efficient compared to a procedure that does not use the ESL cycles because it reduces the total CPU effort to obtain the final design. Also, better final designs are found. The reason is that many more designs are analyzed very efficiently with the ESL procedure.

Background: Peripheral venous catheters which are vital tools when applied correctly and effectively, can cause phlebitis due to many factors. Objectives: To assess the incidence of phlebitis associated with peripheric intravenous catheter and affecting factors in an internal medicine clinic. Methods: This descriptive, cross-sectional study was conducted in December 2018-March 2019 in the internal medicine clinic. The sample consisted of 195 peripheric intravenous catheters on 93 patients. Data was collected by “Patient Information Form” and “Phlebitis Diagnosis Scale”. Chi-square test was used to analyze discrete variable and risk factors were determined by using Logistic Regression analyses. Results: Mean age of the participants was 56.86 ± 18.031 years and 50.5% of them were male. According to the Phlebitis Diagnosis Scale, phlebitis symptoms were observed in 28.2% (n = 55) of the 195 peripheric catheters. Phlebitis incidence was higher in patients aged 66-90 years old (p = .015), patients who had chronic diseases (p = .005), patients who had continuous intravenous infusion (p = .007), patients who were catheterized for 72-96 hours (p = .045), catheters placed on the inactive upper extremity of the patient (p = .012), catheters which were not placed successfully in the first attempt (p = .001), catheters which were placed on a vein which was previously catheterized (p = .001). Conclusion: Phlebitis symptoms were seen in more than one quarter of the patients. Phlebitis incidence was increased in elderly patients with chronic diseases and patients having continuous intravenous infusion, repetitive catheterization in the same vein and prolonged catheterization time. It is recommended for nurses to keep in mind the risk factors for phlebitis development during catheter application and care and to assess the patients with peripheric intravenous catheter regularly with valid and reliable tools and to conduct studies on minimizing the phlebitis development risk., Giriş: Periferik venöz kateterler doğru şekilde uygulandığında yaşamsal önemi olan bir araç olduğu kadar; birçok faktör sebebiyle hastada flebite neden olabilmektedir. Amaç: Bir iç hastalıkları kliniğinde periferik intravenöz kateter ilişkili flebit insidansını ve etkileyen risk faktörlerini belirlemektir. Yöntem: Tanımlayıcı, kesitsel tipte planlanan bu çalışmada, 26 Aralık 2018–30 Mart 2019 tarihleri arasında bir iç hastalıkları kliniğinde 93 hastaya uygulanan 195 periferik intravenöz kateter araştırmanın örneklemini oluşturdu. Veriler “Hasta Bilgi Formu” ve Uluslararası İntravenöz Hemşireler Birliği tarafından kullanılması önerilen “Flebit Tanılama Skalası” ile toplandı. Kategorik değişkenlerin karşılaştırılmasında ki-kare testi, risk faktörlerinin değerlendirilmesinde Lojistik regresyon analizi kullanıldı. Bulgular: Hastaların %50.5’i erkek, yaş ortalaması 56.86 ± 18.031 yıldı. Flebit değerlendirme skalasına göre hastaların %28.2’sinde (n = 55) flebit semptomları saptandı. Yaş grubu 66-90 arasında olan (p = .015), kronik hastalığı olan (p = .005), hastanın aktif olarak kullanmadığı tarafa intravenöz kateterizasyon takılan (p = .012), intravenöz infüzyonu devam eden (p=.007), aynı damara kateterizasyon sıklığı birden fazla olan (p < .001), daha önce aynı damar boyunca kateter takılmış olan (p = .001). ve takılma süresi 72-96 saat olan (p = .045) hastalarda flebit semptomları görülme sıklığı daha fazlaydı. Sonuç: Bu çalışmada periferik intravenöz kateterlerin dörtte birinden daha fazlasında flebit olduğu, ileri yaşın, kronik hastalığın, sürekli infüzyonun, aynı damara birden fazla kateterizasyonun ve kateterin kalış süresinin uzun olmasının hastalarda flebitin görülme oranını artırdığı bulundu. Hemşirelerin flebit gelişimi açısından belirtilen risk faktörlerini kateter uygulaması ve bakımı konusunda göz önünde bulundurmaları, uygulanan periferik intravenöz kateterlerin geçerli ve güvenilir ölçüm araçları ile düzenli olarak flebit belirtileri açısından değerlendirilmesi önerilmektedir.

The random variable of passenger journeys between any two stopping points on a route (passenger correspondence) represents a discrete variable. For each value of the discrete random variable, its probability is calculated. As a solution to the problem of determining the number of corresponding passengers between two stopping points on a route, we take the most probable value of the random variable.

In this article, tourists’ choice of the number of stays (length of stay, a discrete variable) and daily expenditure (a continuous variable) is modelled relaxing the linearity assumption and employing a structural form. A bivariate copula distribution, specified in terms of the marginal distributions of daily tourist expenditure and length of stay, is used to model and test dependence. We propose the Farlie–Gumbel–Morgenstern family of distributions, which provides a powerful tool to build a bivariate distribution with a flexible covariance structure and weak dependence. In addition, covariates can be introduced to study the factors that affect both variables simultaneously. Using Canary Islands Tourist Expenditure Survey data, the estimation results obtained indicate a negative correlation and weak dependence structure between the number of nights’ stay and the daily expenditure. The signs of the coefficients of the socio-economic variables and of the vacation characteristics are generally in line with the findings of empirical literature.

Ospreys (Pandion haliaetus) are adaptable fish-eating raptors that readily nest on artificial structures in heavily human-dominated areas. Although the Osprey is a well-studied species, few researchers have investigated the factors that influence nest success and productivity in an urban environment. We monitored Osprey nests from 2013 to 2017 in highly urbanized Pinellas County, located on the west coast of central Florida, USA. We used logistic exposure models to assess the effects of timing of nesting, nest attributes (nest substrate, height), and landscape-level variables (inter-nest distance, distance to water, and surrounding habitat type) on daily survival rate (DSR) of Osprey nests. The number of active nests (i.e., nests with eggs) in the study area ranged from 53 in 2013 to 79 in 2016, with an overall total of 329 during the 5-yr study. Although most nests produced at least one young near fledging age, 131 of the nests failed. We attributed 45% of nest failures to storm events and 50% to unknown causes. The best logistic exposure model specification included only two variables: the discrete variable representing the date incubation started and the nominal variable indicating the year 2015. Osprey nests initiated earlier in the season were more likely to survive, and later nests (initiated after 22 April) averaged only one fledgling each. Osprey nests in 2015 had the highest DSR and relatively few failed due to storms. Our results supported previous research indicating that early nesters were more successful than late nesters. Our results also indicate that storms may play a role in nest success of Ospreys in Florida. Other variables, such as the amount of urbanized land surrounding Osprey nests did not appear to influence nest survival, indicating that Ospreys can be productive even in highly urban environments.

A discrete variable optimization algorithm is presented based on peloton dynamics that occur during bicycle racing. Peloton dynamics are mainly attributable to the physical capacity of cycl...

This work presents a data-driven design approach to hierarchical hybrid structures with multiple lattice configurations. Two design variables are considered for each lattice substructure, one discrete variable indicating the configuration type and the other continuous density variable determining the geometrical feature size. For each lattice configuration, a series of similar lattice substructures are sampled by varying the density variable and a corresponding data-driven interpolation model is built for an explicit representation of the constitutive behavior. To reduce the model complexity, substructuring by means of static condensation is performed on the sampled lattice substructures. To achieve hybrid structure with multiple lattice configurations, a multi-material interpolation model is adopted by synthesizing the data-driven interpolation models and the discrete lattice configuration variables. The proposed approach has proved capable of generating hierarchically strongly coupled designs, which therefore allows for direct manufacturing with no post-processing requirement as required for homogenization-based designs due to the assumption on scales separation.

The aim of this paper is learning directed acyclic graph (DAG) by determination of candidate causes for each discrete variable. Based on the fact that the candidate causes of a variable must be a s...

Η εξέλιξη των επιχειρήσεων και η ανάπτυξή τους έχει απασχολήσει από παλιά την ακαδημαϊκή κοινότητα (Gibrat 1931). Ένα εξιδεικευμένο τμήμα της βιβλιογραφίας αυτής ασχολείται με τον προσδιορισμό των παραγόντων επιβίωσης των επιχειρήσεων, που αποτελεί αντικείμενο της παρούσας διατριβής. Οι παράγοντες αυτοί μπορεί να αναφέρονται σε ίδια χαρακτηριστικά των επιχειρήσεων και του κλάδου στον οποίο ανήκουν ή και σε μακροοικονομικούς παράγοντες. Ο προαναφερθείς σκοπός επιτυγχάνεται μέσα από την ανάπτυξη των θεωρητικών υποθέσεων με βάση τις οποίες καταρτίζεται το οικονομετρικό υπόδειγμα. Το κύριο βάρος της εργασίας εστιάζεται στην ανάλυση των συνεχών υποδειγμάτων κινδύνου και το έλεγχο των υποθέσεων στα οποία βασίζονται. Ειδικότερα εξετάζεται η επίδραση της μορφής των δεδομένων και της χρονικής συνάθροισης στους εκτιμητές των εφαρμοζόμενων στην μέχρι σήμερα εμπειρική έρευνα υποδειγμάτων. Συγκρίνοντας διαφόρους τύπους διακριτών και συνεχών υποδειγμάτων κινδύνου οδηγούμεθα στο συμπέρασμα ότι τα μέχρι σήμερα εφαρμοζόμενα συνεχή υποδείγματα καταλήγουν σε μεροληπτικά αποτελέσματα. Η εφαρμογή διακριτών υποδειγμάτων κινδύνου PCE, που αποτελεί και την συνεισφορά μας στη βιβλιογραφία, περιορίζει σε σημαντικό βαθμό τα μειονεκτήματα των εφαρμοζόμενων στην εμπειρική έρευνα υποδειγμάτων. Η εφαρμογή της παραπάνω μεθοδολογίας προϋποθέτει δεδομένα τύπου longitudinal τα οποία δεν είναι συνήθως διαθέσιμα. Αυτό εξηγεί το γεγονός των περιορισμένων εμπειρικών εργασιών στο χώρο της επιβίωσης των επιχειρήσεων. Δεδομένης της δυσκολίας εξεύρεσης κατάλληλων δεδομένων η εμπειρική εφαρμογή στηρίχθηκε σε δεδομένα δημοσίων εγγραφών της ελληνικής κεφαλαιαγοράς για την περίοδο 1993-2002. Από όσο είμαστε σε θέση να γνωρίζουμε είναι η πρώτη φορά στη βιβλιογραφία που διεξάγεται παρόμοια έρευνα με ελληνικά δεδομένα δημοσίων εγγραφών. Τέλος, η διατριβή καταλήγει στην εξαγωγή των βασικών συμπερασμάτων και προτάσεων σχετικά με μελλοντική έρευνα.

The present work discusses the implementation of the B92 QKD protocol in MMW using glow discharge device-based single-photon detector.

An algebraic method based on a discrete variable representation (DVR) scheme is applied to describe 1D potentials. The approach is based on the algebraic realisation of the coordinate and momentum ...

We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently-developed reliable numerical methods for key rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols., 25 pages, 9 figures

Effective resource utilization is an important problem in the application of array, especially for the new time modulated array. Considering the problem of full utilization of array elements in time modulated array, a sparse optimization algorithm based on discrete variable convex optimization is proposed in this paper. The pattern optimization of equal excitation time modulation array is realized in two stages: In the first stage, the number of working array elements is as low as possible under the condition of suppressing the sidelobe of the central frequency. In the second stage, the sideband is suppressed by iterative convex optimization. The numerical simulation results are compared with other methods to verify the effectiveness of the proposed method in pattern optimization of equal excitation time modulation array. Finally, the optimization performance of the algorithm with different array parameters is verified.

Algebraic approaches based on a discrete variable representation scheme (DVR) are proposed to describe interatomic effective potentials. The recently proposed unitary group approach (UGA) is identified as a discrete variable representation method among other more general methods discussed in this work. The basic idea consists in establishing an algebraic realisation of the coordinate and momentum in the framework of a dynamical group associated with a complete basis. In the context of the algebraic DVR methods, the discrete coordinate and momentum representations are obtained by diagonalising their matrix representation in a basis associated with a specific potential, in particular, harmonic oscillator, Morse and Pöschl-Teller potentials. This feature provides useful tools to obtain the matrix representation of the Hamiltonian in a simple form through the use of the transformation coefficients connecting the different bases. The proposed algebraic DVR approaches are applied and compared in the framework of 1,2 and 3-D systems. The different approaches are evaluated by considering the Morse, Pöschl-Teller, Kratzer-Fues, Deng-Fan, Varshni and Coulomb potentials., This work is partially supported by DGAPA-UNAM, Mexico (Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México), under project IN-212020, DGAPA UNAM for postdoctoral scholarship (Facultad de Química) to second author, by Spanish Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía [grant numbers FQM-160], and by the Spanish Ministerio de Ciencia e Innovación, ref. FIS2017-88410-P, PID2019-104002GB-C22, and FPA2016-77689-C2-1-R and by the European Commission, ref. H2020-INFRAIA-2014-2015 (ENSAR2). First author is also grateful for the scholarship (Posgrado en Ciencia e Ingeniería de Materiales) provided by CONACyT, México.

In this study, it was aimed to examine the probability problems which were posed based on continuous sample space and discrete sample space. Participants of the study consisted of 48 university students selected by using the convenience sampling method. Eight tasks related to continuous and discrete variables were designed by the researcher. Eight problems posed by each student in accordance with these tasks, their reflection papers and interviews conducted with them constituted the data of the study. Problems were analysed according to appropriateness, solvability, context, applicability, language and variable type dimensions. Findings revealed that most solvable problems were in real-life context, applicable and had clear language. However, most of the unsolvable problems had missing information. Inappropriate problems either were not generated depending on the task instructions or suitable variables were not used in them. Students had difficulties particularly in posing continuous sample space problems. It was concluded that problem posing was an effective practice for students since it enhanced their knowledge about probability and helped them to gain insight into problem posing.

International audience; In addition to the multi-fidelity aspects in MDO discussed in Chapter 8, two additional topics of interest to solve complex MDO problems are discussed in this chapter: multi-objective MDO and mixed continuous/discrete variable design optimization problems.

The article proposes a new analytical method for the calculation of plates with constant and variable rigidity parameters. This method renders it possible to decrease the weight of the plates working under hydrostatic pressure by using variable thicknesses. Firs, a short overview of existing calculation methods and their results are compared. It is shown that all existing methods depend on boundary conditions. Then is given the theory of the proposed calculation method is described and calculations for plates with constant and variable thickness worked under uniformly loaded forces and hydrostatic pressure are made. The results are compared to the FEM calculations and experimental results obtained by a tensile test machine and special equipment. Calculation results obtained by the proposed analytical method and FEM results are very close. Deviations are not more than 11%. Deviations between theoretical calculations and experimental results depend on loading type and design of the test specimens but maximum values are not more than 17%. The proposed calculation method does not depend on the boundary conditions and can be used for plate calculations. Especially for plates with difficult design and complex loading.

The Time Dependent Discrete Variable Representation (TDDVR) method was initiated by Adhikari and Billing considering time dependent Gauss-Hermite basis functions, where all the parameters w...

Two finite hypergeometric sequences of symmetric orthogonal polynomials of a discrete variable are introduced and their standard properties, such as second-order difference equations, expli...

We derive auto-Backlund transformations, analogous to those of the matrix second Painleve equation, for a matrix partial differential equation. We also then use these auto-Backlund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Backlund transformations of the matrix second Painleve equation to derive a discrete matrix first Painleve equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painleve equation. The application of this technique to the auto-Backlund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painleve equation, and which does not seem to have been thus derived previously.

Some discrete variable such as frequency cannot be estimated when a limited sample is drawn from the population which is not sufficient enough to represent the whole population. But the procedure records data from finite samples that can be converted to frequency estimates through computer intensive calculations. The aim of this paper is to develop an Accelerated Failure Time model for the continuous variables such as survival times or the first breakdown mileage by embedding Weibull distribution into a GLMs structure. Then we can derive the hazard ratio function and transform the continuous variable modeling into discrete variable inference. A numerical illustration based on a data derived from a Chinese auto dealer is performed with the statistical software SAS. The rate was made for different types of vehicles and their different parts based on the minimum repairing and the purchase of car repairing insurance for a certain time.

The aim of our study was to examine the combined effect of NaCl and low temperature on antilisterial bacteriocin production of L. plantarum. Traditionally, the activity of the bacteriocin (arbitrary unit/ml) is determined as an adaptation of the critical dilution method. With that methodology, the value of AU/ml is a discrete variable, which may cause information loss. Therefore, redox potential measurement technique was applied. Bacteriocin producer L. plantarum and a bacteriocin sensitive L. monocytogenes strain were selected for this study. The measure of the inhibition activity of bacteriocin was expressed in ΔTTD terms which means the difference between the detection times of L. monocytogenes in inhibited and non-inhibited culture media. During the L. plantarum fermentations the antilisterial activity proved to be the highest in the transient section between the late linear and stationer phase of the logarithmic growth curves. Multiple regression model was established to describe the combined effect of temperature and NaCl concentration on the bacteriocin production of L. plantarum.