Dynamics of hydrogen-like atom bounded by maximal acceleration

The existence of a maximal acceleration for massive objects was conjectured by Caianiello 30 years ago based on the Heisenberg uncertainty relations. Many consequences of this hypothesis have been studied, but until now, there has been no evidence that boundedness of the acceleration may lead to quantum behavior. In previous research, we predicted the existence of a universal maximal acceleration and developed a new dynamics for which all admissible solutions have an acceleration bounded by the maximal one. Based on W. K\"{u}ndig's experiment, as reanalyzed by Kholmetskii et al, we estimated its value to be of the order $10^{19}m/s^2$. We present here a solution of our dynamical equation for a classical hydrogen-like atom and show that this dynamics leads to some aspects of quantum behavior. We show that the position of an electron in a hydrogen-like atom can be described only probabilistically. We also show that in this model, the notion of "center of mass" must be modified. This modification supports the non-existence of a magnetic moment in the atom and explains the relevance of the conformal group in the quantum region.Comment: 10 pages, 1 figur

An efficient RAN slicing strategy for a heterogeneous network with eMBB and V2X services

Emerging 5G wireless technology will support services and use cases with vastly heterogeneous requirements. Network slicing, which allows composing multiple dedicated logical networks with specific functionality running on top of a common infrastructure, is introduced as a solution to cope with this heterogeneity. At the radio access network (RAN), the use of network slicing involves the assignment of radio resources to each slice in accordance with its expected requirements and functionalities. Therefore, RAN slicing will provide the required design flexibility and will be necessary for any network slicing solution. This paper investigates the RAN slicing problem for providing two generic services of 5G, namely enhanced mobile broadband (eMBB) and vehicle-to-everything (V2X). In this respect, we propose an efficient RAN slicing scheme based on an off-line reinforcement learning followed by a low-complexity heuristic algorithm, which allocates radio resources to different slices with the target of maximizing the resource utilization while ensuring the availability of resources to fulfill the requirements of the traffic of each RAN slice. A simulation-based analysis is presented to assess the performance of the proposed solution. The simulation results have shown that the proposed algorithm improves the network performance in terms of resource utilization, the latency of V2X services, achievable data rate, and outage probability.Peer ReviewedPostprint (published version

A Simple Algorithm for Exact Multinomial Tests

This work proposes a new method for computing acceptance regions of exact multinomial tests. From this an algorithm is derived, which finds exact p-values for tests of simple multinomial hypotheses. Using concepts from discrete convex analysis, the method is proven to be exact for various popular test statistics, including Pearson’s Chi-square and the log-likelihood ratio. The proposed algorithm improves greatly on the naive approach using full enumeration of the sample space. However, its use is limited to multinomial distributions with a small number of categories, as the runtime grows exponentially in the number of possible outcomes. The method is applied in a simulation study, and uses of multinomial tests in forecast evaluation are outlined. Additionally, properties of a test statistic using probability ordering, referred to as the “exact multinomial test” by some authors, are investigated and discussed. The algorithm is implemented in the accompanying R package ExactMultinom. Supplementary materials for this article are available online

From Classification Accuracy to Proper Scoring Rules: Elicitability of Probabilistic Top List Predictions

In the face of uncertainty, the need for probabilistic assessments has long been recognized in the literature on forecasting. In classification, however, comparative evaluation of classifiers often focuses on predictions specifying a single class through the use of simple accuracy measures, which disregard any probabilistic uncertainty quantification. I propose probabilistic top lists as a novel type of prediction in classification, which bridges the gap between single-class predictions and predictive distributions. The probabilistic top list functional is elicitable through the use of strictly consistent evaluation metrics. The proposed evaluation metrics are based on symmetric proper scoring rules and admit comparison of various types of predictions ranging from single-class point predictions to fully specified predictive distributions. The Brier score yields a metric that is particularly well suited for this kind of comparison

Model Diagnostics meets Forecast Evaluation: Goodness-of-Fit, Calibration, and Related Topics

Principled forecast evaluation and model diagnostics are vital in fitting probabilistic models and forecasting outcomes of interest. A common principle is that fitted or predicted distributions ought to be calibrated, ideally in the sense that the outcome is indistinguishable from a random draw from the posited distribution. Much of this thesis is centered on calibration properties of various types of forecasts. In the first part of the thesis, a simple algorithm for exact multinomial goodness-of-fit tests is proposed. The algorithm computes exact $p$-values based on various test statistics, such as the log-likelihood ratio and Pearson\u27s chi-square. A thorough analysis shows improvement on extant methods. However, the runtime of the algorithm grows exponentially in the number of categories and hence its use is limited. In the second part, a framework rooted in probability theory is developed, which gives rise to hierarchies of calibration, and applies to both predictive distributions and stand-alone point forecasts. Based on a general notion of conditional T-calibration, the thesis introduces population versions of T-reliability diagrams and revisits a score decomposition into measures of miscalibration, discrimination, and uncertainty. Stable and efficient estimators of T-reliability diagrams and score components arise via nonparametric isotonic regression and the pool-adjacent-violators algorithm. For in-sample model diagnostics, a universal coefficient of determination is introduced that nests and reinterprets the classical $R^2$ in least squares regression. In the third part, probabilistic top lists are proposed as a novel type of prediction in classification, which bridges the gap between single-class predictions and predictive distributions. The probabilistic top list functional is elicited by strictly consistent evaluation metrics, based on symmetric proper scoring rules, which admit comparison of various types of predictions

A Simple Algorithm for Exact Multinomial Tests

This work proposes a new method for computing acceptance regions of exact multinomial tests. From this an algorithm is derived, which finds exact p-values for tests of simple multinomial hypotheses. Using concepts from discrete convex analysis, the method is proven to be exact for various popular test statistics, including Pearson's chi-square and the log-likelihood ratio. The proposed algorithm improves greatly on the naive approach using full enumeration of the sample space. However, its use is limited to multinomial distributions with a small number of categories, as the runtime grows exponentially in the number of possible outcomes. The method is applied in a simulation study and uses of multinomial tests in forecast evaluation are outlined. Additionally, properties of a test statistic using probability ordering, referred to as the "exact multinomial test" by some authors, are investigated and discussed. The algorithm is implemented in the accompanying R package ExactMultinom.Comment: 27 page

Synthesis and Characterization of 1-(4-Choro Phenyl )-3-(Pyrimidin -2-yl) Thiourea and its Complexes with Cobalt(II) , Nickel(II), and Copper(II)

The new 1-(4-chloro phenyl )-3-(pyrimidin -2-yl) thiourea was synthesized from the condensation reaction of 2- amino pyrimidin with p-chlorophenyl isothiocyanate. The complexes were prepared from the reaction of the metal chloride with the ligand. The ligand  and its metal complexes were characterized by spectroscopic methods (FTIR , UV-Vis , 1H-NMR , A.A) , magnetic measurements , conductance and melting point. These studies revealed square planar geometries for the Co(II), Ni(II) and Cu(II) complexes. Keywords: 2- amino pyrimidin; p-chlorophenyl isothiocyanate and thiourea complexes.

MODIFIKASI TEORITIK STRUKTUR JEMBATAN π ZAT WARNA TIPE D-π-A SEBAGAI SENSITIZER PADA SEL SURYA BERBASIS FENOL

Salah satu jenis teknologi berbasis sel surya ialah Dye Sensitized Solar Cell (DSSC). Pada penelitian terkait DSSC zat warna menjadi topik paling banyak diteliti karena dengan memodifikasi struktur dari zat warna maka akan dapat meningkatkan kinerja dan efisiensi dari DSSC. Zat warna organik merupakan sensitizer (pemeka cahaya) yang sangat cocok digunakan untuk perangkat DSSC karena ramah lingkungan, berlimpah dan minim biaya. Pada penelitian ini menggunakan fenol sebagai basis dan memvariasikan jembatan π dari molekul zat warna tipe D-π-A (Donor – Jembatan π – Akseptor). Jembatan π yang digunakan diantaranya butadiena, heksatriena, antrasena, fenantrena, bifuran dan bithiopen yang disimbolkan dengan Fπ1, Fπ2, Fπ3, Fπ4, Fπ5 dan Fπ6. Penelitian ini menggunakan Gaussian 16W sebagai program utama, Density Functional Theory (DFT) dan Time Dependent-DFT (TD-DFT) merupakan metode perhitungan dengan basis B3LYP/6-31G. Dalam menentukan efisiensi dari molekul zat warna sebagai sensitizer pada perangkat DSSC maka parameter perhitungan yang digunakan ialah serapan panjang gelombang maksimum (λmaks), nilai bandgap, energi eksitasi, ∆Ginj, ∆Greg, momen dipol, oscillator strength (f), tegangan (VOC), dan nilai Light Harvesting Efficiency (LHE). Berdasarkan hasil penelitian, zat warna Fπ6 dengan variasi jembatan π bithiopen merupakan zat warna terbaik untuk dijadikan sebagai sensitizer dengan nilai bandgap 2,77 eV dan λ sebesar 456,96 nm menunjukkan zat warna mampu menyerap energi sinar tampak dari cahaya matahari. Sedangkan nilai momen dipol 9,78 D, energi eksitasi 2,71 eV, ΔGinj -1,39 eV, ΔGreg 0,52 eV, dan nilai VOC 1,44 eV menunjukkan semakin mudahnya proses transfer elektron pada zat warna dan dari zat warna ke perangkat DSSC