Experimental study of Forrelation in nuclear spins

We prove rigorously, in the general case of arbitrary potential and number of components, that if a solution of the mean spherical approximation for simple fluids exists it is unique within the class of correlation functions corresponding to positive and bounded structure factors. The longstanding problem of the choice of the acceptable solutions of the system of nonlinear algebraic equations which arises with some methods used to derive analytical solutions is carefully examined with a particular emphasis on the factorization method for Yukawa mixtures. It is shown that a local criterion, related to the boundedness of the pair correlation functions, already suggested by Baxter but apparently ignored in the recent literature, is sufficient to select the unique (acceptable) solution of the model. A very simple and practical implementation of the method is given. The dependence of the asymptotic behaviour of the pair correlation functions on the parameters is briefly discussed.

The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only “balanced” or “tilted” information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a measure for the cost of weighing algorithms (the number of weighings). In this paper, we study the quantum query complexity for this problem. Let Q(k,N) be the quantum query complexity of finding all k false coins from the N given coins. We show that for any k and N such that k < N/2, Q(k,N) = O(k 1/4), contrasting with the classical query complexity, Ω(klog(N/k)), that depends on N. So our quantum algorithm achieves a quartic speed-up for this problem. We do not have a matching lower bound, but we show some evidence that the upper bound is tight: any algorithm, including our algorithm, that satisfies certain properties needs Ω(k 1/4) queries.

Preparing a data set for analysis is generally the most time consuming task in a data mining project, requiring many complex SQL queries, joining tables and aggregating columns. Existing SQL aggregations have limitations to prepare data sets because they return one column per aggregated group. In general, a significant manual effort is required to build data sets, where a horizontal layout is required. We propose simple, yet powerful, methods to generate SQL code to return aggregated columns in a horizontal tabular layout, returning a set of numbers instead of one number per row. This new class of functions is called horizontal aggregations. Horizontal aggregations build data sets with a horizontal denormalized layout (e.g. point-dimension, observation-variable, instance-feature), which is the standard layout required by most data mining algorithms. We propose three fundamental methods to evaluate horizontal aggregations: CASE: Exploiting the programming CASE construct; SPJ: Based on standard relational algebra operators (SPJ queries); PIVOT: Using the PIVOT operator, which is offered by some DBMSs. Experiments with large tables compare the proposed query evaluation methods. Our CASE method has similar speed to the PIVOT operator and it is much faster than the SPJ method. In general, the CASE and PIVOT methods exhibit linear scalability, where as the SPJ method does not. In a relational database, especially with normalized tables, a significant effort is required to prepare a summary data set that can be used as input for a data mining or statistical algorithm. Most algorithms require as input a data set with a horizontal layout, with several Records and one variable or dimension per column. That is the case with models like clustering, classification, regression and PCA; consult. Each research discipline uses different terminology to describe the data set. In data mining the common terms are point-dimension. Statistics literature generally uses observation-variable. Machine learning research uses instance-feature. This article introduces a new class of aggregate functions that can be used to build data sets in a horizontal layout (denormalized with aggregations), automating SQL query writing and extending SQL capabilities. We show evaluating horizontal aggregations is a challenging and interesting problem and we introduced alternative methods and optimizations for their efficient evaluation. II. MOTIVATION As mentioned above, building a suitable data set for data mining purposes is a time- consuming task. This task generally requires writing long SQL statements or customizing SQL Code if it is automatically generated by some tool. There are two main ingredients in such SQL code: joins and aggregations; we focus on the second one. The most widely- known aggregation is the sum of a column over groups of rows. Some other aggregations return the average, maximum, minimum or row count over groups of rows. There exist many aggregations functions and operators in SQL. Unfortunately, all these aggregations have limitations to build data sets for data mining purposes. The main reason is that, in general, data sets that are stored in a relational database (or a data warehouse) come

Differences in urban design features may affect emission and dispersion patterns of air pollution at local-scales within cities. However, the complexity of urban forms, interdependence of variables, and temporal and spatial variability of processes make it difficult to quantify determinants of local-scale air pollution. This paper uses a combination of dense measurements and a novel approach to land-use regression (LUR) modeling to identify key controls on concentrations of ambient nitrogen dioxide (NO2) at a local-scale within a central business district (CBD). Sixty-two locations were measured over 44 days in Auckland, New Zealand at high density (study area 0.15 km(2)). A local-scale LUR model was developed, with seven variables identified as determinants based on standard model criteria. A novel method for improving standard LUR design was developed using two independent data sets (at local and "city" scales) to generate improved accuracy in predictions and greater confidence in results. This revised multiscale LUR model identified three urban design variables (intersection, proximity to a bus stop, and street width) as having the more significant determination on local-scale air quality, and had improved adaptability between data sets.

It has recently been shown that quantum computers can efficiently solve the Heisenberg hidden subgroup problem, a problem whose classical query complexity is exponential. This quantum algorithm was...

While radiologists regularly issue follow-up recommendations, our preliminary research has shown that anywhere from 35 to 50% of patients who receive follow-up recommendations for findings of possible cancer on abdominopelvic imaging do not return for follow-up. As such, they remain at risk for adverse outcomes related to missed or delayed cancer diagnosis. In this study, we develop an algorithm to automatically detect free text radiology reports that have a follow-up recommendation using natural language processing (NLP) techniques and machine learning models. The data set used in this study consists of 6000 free text reports from the author's institution. NLP techniques are used to engineer 1500 features, which include the most informative unigrams, bigrams, and trigrams in the training corpus after performing tokenization and Porter stemming. On this data set, we train naive Bayes, decision tree, and maximum entropy models. The decision tree model, with an F1 score of 0.458 and accuracy of 0.862, outperforms both the naive Bayes (F1 score of 0.381) and maximum entropy (F1 score of 0.387) models. The models were analyzed to determine predictive features, with term frequency of n-grams such as "renal neoplasm" and "evalu with enhanc" being most predictive of a follow-up recommendation. Key to maximizing performance was feature engineering that extracts predictive information and appropriate selection of machine learning algorithms based on the feature set.

An experiment demonstrating the quantum simulation of a spin-lattice Hamiltonian is proposed. Dipolar interactions between nuclear spins in a solid state lattice can be modulated by rapid radio-frequency pulses. In this way, the effective Hamiltonian of the system can be brought to the form of an antiferromagnetic Heisenberg model with long range interactions. Using a semiconducting material with strong optical properties such as InP, cooling of nuclear spins could be achieved by means of optical pumping. An additional cooling stage is provided by adiabatic demagnetization in the rotating frame down to a nuclear spin temperature at which we expect a phase transition from a paramagnetic to antiferromagnetic phase. This phase transition could be observed by probing the magnetic susceptibility of the spin lattice. Our calculations suggest that employing current optical pumping technology, observation of this phase transition is within experimental reach.

Nuclear spin rates of relaxation due to magnetic dipole coupling between spins undergoing relative translational diffusion in single crystals will depend on the orientation of the applied static magnetic field with respect to the crystal axes. The general form of the orientation dependence is calculated for the nuclear spin correlation functions J(q)( omega ) and hence for the relaxation rates and the second moment of a rigid-lattice absorption line broadened by dipolar interactions. The only assumption concerning the diffusional motion is the principle of detailed balance and the orientation dependence is obtained using the transformation properties of spherical harmonics in terms of rotation matrices. Explicit results are obtained for the correlation functions and relaxation rates for each point group and the form of the relaxation rates in the low-frequency (high-temperature) limit is deduced.

It is known that the classical and quantum query complexities of a total Boolean function f are polynomially related to the degree of its representing polynomial, but the optimal exponents in these relations are unknown. We show that the quantum query complexity of f is linearly related to the degree of a non-deterministic polynomial for f. We also prove a quantum-classical gap of 1 vs. N for query complexity for a total f. In the case of quantum communication complexity there is a (partly undetermined) relation between the complexity of f and the logarithm of the rank of its communication matrix. We show that the quantum communication complexity of f is linearly related to the logarithm of the rank of a version of the communication matrix and that it can be exponentially smaller than its classical counterpart.

The effect of paramagnetic impurities with local moments on the nuclear-spin-lattice relaxation is studied by using the method of Blume and Hubbard. An average over random impurities is taken on the equations of motion for nuclear and electron spins in the low-concentration limit. An integral equation for the electron-spin correlation function is obtained and solved self-consistently. The correlation function behaves like $\mathrm{exp}[\ensuremath{-}{(\frac{t}{{\ensuremath{\Gamma}}_{1}})}^{2}]$ for small $t$, $\mathrm{exp}[\ensuremath{-}(\frac{t}{{\ensuremath{\Gamma}}_{2}})]$ for intermediate $t$, and $\mathrm{exp}[\ensuremath{-}{(\frac{t}{{\ensuremath{\Gamma}}_{3}})}^{\frac{1}{2}}]$ for large $t$. The nuclear-spin correlation function is calculated from the electron-spin correlation function. The dependence of the spin-lattice relaxation time on the concentration of impurities, magnetic field; and temperature is obtained. Our calculations are discussed in terms of results obtained from the phenomenological approach.

Preparing a data set for analysis is generally the most time consuming task in a data mining project, requiring many complex SQL queries, joining tables, and aggregating columns. Existing SQL aggregations have limitations to prepare data sets because they return one column per aggregated group. In general, a significant manual effort is required to build data sets, where a horizontal layout is required. We propose simple, yet powerful, methods to generate SQL code to return aggregated columns in a horizontal tabular layout, returning a set of numbers instead of one number per row. This new class of functions is called horizontal aggregations. Horizontal aggregations build data sets with a horizontal denormalized layout (e.g., point-dimension, observation-variable, instance-feature), which is the standard layout required by most data mining algorithms. We propose three fundamental methods to evaluate horizontal aggregations: CASE: Exploiting the programming CASE construct; SPJ: Based on standard relational algebra operators (SPJ queries); PIVOT: Using the PIVOT operator, which is offered by some DBMSs. Experiments with large tables compare the proposed query evaluation methods. Our CASE method has similar speed to the PIVOT operator and it is much faster than the SPJ method. In general, the CASE and PIVOT methods exhibit linear scalability, whereas the SPJ method does not.

Nowadays, there is a huge increase in digital financial fraud as a result of the widespread usage of credit cards for online purchases. Therefore, a credit card fraud detection method with high accuracy, minimizing the risk of losing money when the transaction occurs, becomes imperative. The study first processed a synthetic data set, discarding useless features, using one hot encoding to convey categorical information to numerical ones and separating the training and testing datasets. Based on the new formed datasets, the study built three Machine Learning (ML) models for fraud detection, which are the Support Vector Machine (SVM) model, the logistic regression model and the decision tree model, respectively. Next, the study implemented on training these three models by fitting the model on training datasets and predicting the test data in testing datasets. Lastly, the heatmap named confusion matrix was provided to visualize the outcomes, indicating the accuracy of each model. Also, the study uses another four performance measurement scores which are Area under the Receiver Operating Characteristic Curve (ROC AUC score), accuracy classification score, balanced F1 score and precision score for evaluating models. Comparing these three models based on the confusion matrix and the four accuracy scores, the study explored that the decision tree model can achieve the best performance compared to other models in predicting fraud.

Time series classification (TSC) is an important and challenging problem in data mining. Time series data sets are an important basis for this research and are widely used in baseline verification of various algorithm models. Aiming at the problem that there are few domestic data sets and the current TSC data set is relatively old, a new set of time‐series classification datasets are established based on the average price data of concrete in major cities in China, which provides new data support for the research of TSC algorithm. We made use of the data center of Oriental Fortune to disclose the sample data of the average price of concrete from October 23, 2013 to January 20, 2021, created 1093 autoregression‐based series data sets by using sliding windows of different lengths, and then through the experimental verification of linear regression model, decision tree model, and random forest model, a set of data sets with lengths of 170, 842, and 1052 were selected. We use three convolutional neural network (CNN) models and three long short‐term memory (LSTM) network models to verify the validity of the data, the CNN's obtained the best accuracy rate of 93.20%, and the LSTM networks obtained the best accuracy rate of 92.99%. The establishment of the new data set has certain significance for the research of TSC and provides some references for other researchers to create datasets. The datasets are freely available at https://gitee.com/lq2012/tsc‐dataset.

We present a method for measuring single spins embedded in a solid by probing two electron systems with a single electron transistor (SET). Restrictions imposed by the Pauli Principle on allowed two electron states mean that the spin state of such systems has a profound impact on the orbital states (positions) of the electrons, a parameter which SET's are extremely well suited to measure. We focus on a particular system capable of being fabricated with current technology: a Te double donor in Si adjacent to a Si/SiO2 interface and lying directly beneath the SET island electrode, and we outline a measurement strategy capable of resolving single electron and nuclear spins in this system. We discuss the limitations of the measurement imposed by spin scattering arising from fluctuations emanating from the SET and from lattice phonons. We conclude that measurement of single spins, a necessary requirement for several proposed quantum computer architectures, is feasible in Si using this strategy.

Targeting at the realization of scalable photonic quantum technologies, the generation of many photons, their propagation in large optical networks, and a subsequent detection and analysis of sophisticated quantum correlations are essential for the understanding of macroscopic quantum systems. In this experimental contribution, we explore the joint operation of all mentioned ingredients. We benchmark our time-multiplexing framework that includes a high-performance source of multiphoton states and a large multiplexing network, together with unique detectors with high photon-number resolution, readily available for distributing quantum light and measuring complex quantum correlations. Using an adaptive approach that employs flexible time bins, rather than static ones, we successfully verify high-order nonclassical correlations of many photons distributed over many modes. By exploiting the symmetry of our system and using powerful analysis tools, we can analyze correlations that would be inaccessible by classical means otherwise. In particular, we produce on the order of ten photons and distribute them over 64 modes. Nonclassicality is verified with correlation functions up to the 128th order and statistical significances of up to 20 standard deviations.