Exact Expectation Research Articles

Fast Context-Aware Analysis of Genome Annotation Colocalization.

An annotation is a set of genomic intervals sharing a particular function or property. Examples include genes or their exons, sequence repeats, regions with a particular epigenetic state, and copy number variants. A common task is to compare two annotations to determine if one is enriched or depleted in the regions covered by the other. We study the problem of assigning statistical significance to such a comparison based on a null model representing random unrelated annotations. To incorporate more background information into such analyses, we propose a new null model based on a Markov chain that differentiates among several genomic contexts. These contexts can capture various confounding factors, such as GC content or assembly gaps. We then develop a new algorithm for estimating p-values by computing the exact expectation and variance of the test statistic and then estimating the p-value using a normal approximation. Compared to the previous algorithm by Gafurov et al., the new algorithm provides three advances: (1) the running time is improved from quadratic to linear or quasi-linear, (2) the algorithm can handle two different test statistics, and (3) the algorithm can handle both simple and context-dependent Markov chain null models. We demonstrate the efficiency and accuracy of our algorithm on synthetic and real data sets, including the recent human telomere-to-telomere assembly. In particular, our algorithm computed p-values for 450 pairs of human genome annotations using 24 threads in under three hours. Moreover, the use of genomic contexts to correct for GC bias resulted in the reversal of some previously published findings.

Synergy between noisy quantum computers and scalable classical deep learning for quantum error mitigation

We investigate the potential of combining the computational power of noisy quantum computers and of classical scalable convolutional neural networks (CNNs). The goal is to accurately predict exact expectation values of parameterized quantum circuits representing the Trotter-decomposed dynamics of quantum Ising models. By incorporating (simulated) noisy expectation values alongside circuit structure information, our CNNs effectively capture the underlying relationships between circuit architecture and output behaviour, enabling, via transfer learning, also predictions for circuits with more qubits than those included in the training set. Notably, thanks to the quantum information, our CNNs succeed even when supervised learning based only on classical descriptors fails. Furthermore, they outperform a popular error mitigation scheme, namely, zero-noise extrapolation, demonstrating that the synergy between quantum and classical computational tools leads to higher accuracy compared with quantum-only or classical-only approaches. By tuning the noise strength, we explore the crossover from a computationally powerful classical CNN assisted by quantum noisy data, towards rather precise quantum computations, further error-mitigated via classical deep learning.

Testing rational expectations in a cointegrated VAR with structural change

The rational expectation hypothesis is widely used in finance and macroeconomics. A research question investigates whether models using this hypothesis can fit the data well. Researchers have been developing econometric procedures to test rational expectation models. Sargent and Hansen (1991) proposed how to test exact rational expectation restrictions. This study aims to achieve three objectives. The first objective is to extend Johansen and Swensen’s framework that test exact rational expectation restrictions to the case where the data-generating process is a cointegrated vector autoregressive model with abrupt structural change (CVAR-SC). The second goal is to highlight that the type of rational expectation restrictions analysed in this paper imply co-breaking, as defined by Hendry and Mizon (1998). Finally, the restrictions on the CVAR-SC parameters implied by the present value model and expectation hypothesis of the interest rate term structure are analysed, derived and tested. Three empirical exercises are reported. The first is Engsted (2002)’s dataset on share prices and dividends, the second uses a Brazilian term structure data set and the third uses a North American term structure dataset.

Stability analysis of the bias compensated LMS algorithm

The presence of noise is a pervasive issue that significantly impacts the performance of adaptive filtering algorithms. To address this challenge, the bias compensation technique has recently emerged, involving the incorporation of an additional term into the update equation. Despite the apparent simplicity of the bias-compensated least-mean-squares algorithm, conducting a comprehensive theoretical analysis of its performance is a complex task. In this paper, we undertake an exact expectation analysis to demonstrate the asymptotic unbiasedness of the algorithm, even when disregarding the commonly assumed theory of independence between adaptive coefficients and input data. Furthermore, to improve the understanding of the algorithm's stability, we employ a stochastic model that assumes independence between the radial and angular distributions of the input vector. The resulting model is intricate, necessitating heuristic approximations to derive practical insights. Notably, our analysis reveals that the upper bound on the step size of the bias-compensated least-mean-squares algorithm consistently remains smaller than that of the least-mean-squares algorithm. These findings gain robust support from extensive simulations.

The complexity of quantum support vector machines

Quantum support vector machines employ quantum circuits to define the kernel function. It has been shown that this approach offers a provable exponential speedup compared to any known classical algorithm for certain data sets. The training of such models corresponds to solving a convex optimization problem either via its primal or dual formulation. Due to the probabilistic nature of quantum mechanics, the training algorithms are affected by statistical uncertainty, which has a major impact on their complexity. We show that the dual problem can be solved in O(M4.67/ε2) quantum circuit evaluations, where M denotes the size of the data set and ε the solution accuracy compared to the ideal result from exact expectation values, which is only obtainable in theory. We prove under an empirically motivated assumption that the kernelized primal problem can alternatively be solved in O(min{M2/ε6,1/ε10}) evaluations by employing a generalization of a known classical algorithm called Pegasos. Accompanying empirical results demonstrate these analytical complexities to be essentially tight. In addition, we investigate a variational approximation to quantum support vector machines and show that their heuristic training achieves considerably better scaling in our experiments.

Analysis of the least mean squares algorithm with reusing coefficient vector

The coefficient reuse strategy is able to improve the steady-state performance of adaptive filter algorithms, especially in very challenging low signal-to-noise scenarios. This paper advances deterministic and stochastic models that predict various learning characteristics of the LMS algorithm with coefficient reuse. First-order and second-order analyzes are derived for the sufficient order case and then extended for the tracking and deficient length scenarios. An exact expectation analysis, which does not employ the ubiquitous independence assumption, is presented for a particular configuration of the algorithm, and its results suggest that, except in the first phase of the learning process, the decay in mean-square deviation of the coefficient vector is governed by an almost-sure theoretical analysis. The simulation results confirm the equations obtained in the theoretical analysis.

Quantum mean-value approximator for hard integer-value problems

Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum eigensolvers. We show that such an optimization can be improved substantially by using an approximation rather than the exact expectation. Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems, such as the shortest vector problem (SVP) investigated in this work.

Approximate formulas for the evaluation of the mathematical expectation of functionals from the solution to the linear Skorohod equation

This paper is devoted to the construction of approximate formulas for calculating the mathematical expectation of nonlinear functionals from the solution to the linear Skorohod stochastic differential equation with a random initial condition. To calculate the mathematical expectations of nonlinear functionals from random processes, functional analogs of quadrature formulas have been developed, based on the requirement of their accuracy for functional polynomials of a given degree. Most often, formulas are constructed that are exact for polynomials of the third degree [1–9], which are used to obtain an initial approximation and in combination with approximations of the original random process. In the latter case, they are usually also exact for polynomials of a given degree and are called compound formulas. However, in the case of processes specified in the form of compound functions from other random processes the constructed functional quadrature formulas, as a rule, have great computational complexity and cannot be used for computer implementation. This is exactly what happens in the case of functionals from the solutions of stochastic equations. In [1, 2], the approaches to solving this problem were considered for some types of Ito equations in martingales. The solution of the problem is simplified in the cases when the solution of the stochastic equation is found in explicit form: the corresponding approximations were obtained in the cases of the linear equations of Ito, Ito – Levy and Skorohod in [3–11]. In [7, 8, 11], functional quadrature formulas were constructed that are exact for the approximations of the expansions of the solutions in terms of orthonormal functional polynomials and in terms of multiple stochastic integrals. This work is devoted to the approximate calculation of the mathematical expectations of nonlinear functionals from the solution of the linear Skorokhod equation with a leading Wiener process and a random initial condition. A new approach to the construction of quadrature formulas, exact for functional polynomials of the third degree, based on the use of multiple Stieltjes integrals over functions of bounded variation in the sense of Hardy – Krause, is proposed. A composite approximate formula is also constructed, which is exact for second-order functional polynomials, converging to the exact expectation value, based on a combination of the obtained quadrature formula and an approximation of the leading Wiener process. The test examples illustrating the application of the obtained formulas are considered.

DEVELOPING AN INTEGRATED MODEL BASED ON AUTOMATED TOOLS FOR AN EARLY DETECTION AND DIAGNOSIS OF CANCER RISK

Malignancy can start in any part of the body and can spread to different factors too. It is wild, and it has many sorts. The proposed theory research paper presents a device for foreseeing some disease risks with five unique malignancy determinations and proposals. For perceiving should need malignant growth sickness number of tests from the patient. In any case, utilizing information mining procedures can reduce these tests. To be sure, an exact expectation of malignancy is an undeniably challenging undertaking for the clinical expert. It is likewise a profound worry to the patients to give better treatment, and it will again build the endurance season of the patients. Our discoveries proposed that a reasonable forecast instrument can successfully diminish the few tests for diagnosing malignant growth and expectation exactness, subsequently expanding the specialized chance of early disease identification. The apparatus's principle highlights harmony between the quantity of important data sources and forecast execution, being versatile, and engaging the programmed improvement of the malignant growth hazard expectation instrument in malignant growth illness.

Adjustment coefficients and exact rational expectations in cointegrated vector autoregressive models

In cointegrated vector autoregressive models exact linear rational expectation relations can imply restrictions on the adjustment parameters. We show how such restrictions can be tested, in particular when the restrictions imply weak exogeneity of some variables.

Prediction of Cardiovascular Disease using Artificial Neural Network

The determination of coronary illness much of the time relies upon an unpredictable blend of clinical and neurotic information. Inlight of this intricacy, there exists a lot of revenue among clinical experts and analysts in regards to the productive and exact expectation of coronary illness. In this paper, we foster a coronary illness foresee framework that can help clinical experts in anticipating coronary illness status dependent on the clinical information of patients. AI grouping methods are incredibly helpful in the clinical field by giving exact outcomes and fast conclusion of illnesses. Consequently, these procedures save part of time for the two specialists and patients. The neural organizations can be utilized as classifiers anticipate the determination of Cardiovascular Heart sickness.

On the Skewness of the LMS Adaptive Weights

The adjustable weights of adaptive filtering algorithms are usually assumed to obey a Gaussian distribution. This is somewhat natural under maximal-entropy considerations, since most analyses in the open literature only take into account first-and second-order statistics. This work investigates the third-order statistical feature known as skewness of the least mean square parameters distribution. Two theoretical analyses for skewness estimation are proposed: i) one that employs the independence assumption, which states that the excitation data is statistically independent from the adaptive weights; ii) one derived from the exact expectation analysis, a method that is able to predict the learning capabilities of the least mean square algorithm even when the step size is not infinitesimally small. This brief shows that the skewness of the adaptive weights distribution may present a large deviation from the common Gaussian assumption, especially in the first phase of the learning. Furthermore, it is also demonstrated that the skewness may grow without limit even when adaptive weights present convergence in both average and mean square behaviors.

Optimal energy management of residential battery storage under uncertainty

Backgroud The uncertainty associated with renewable generation and loads imposes various challenges for the economic operation of microgrids. On the residential side, energy storage systems are implemented with high expectations to enhance photovoltaic power consumption and electricity price arbitrage. Aims This paper proposes an expectation-oriented stochastic model for optimal energy management of household batteries to cope with the uncertain electricity generation and consumption. Materials & Methods The exact cost expectation of daily operation is formulated as an alternative to the conventional scenario-based average approximation. A predictive control-based battery scheduling mechanism is developed further to apply the proposed model to intraday energy storage management. Results Simulation results validate the convexity of the proposed model. Discussion Although nonlinear in nature, the resultant optimization problem is proven to be convex, which ensures computable global optimal solutions for the proposed model. Conclusion Simulation results demonstrate the effectiveness of the proposed scheduling strategy compared with existing methods.

Prognosticate of the financial market utilizing ensemble-based conglomerate model with technical indicators

The financial exchange is known for its outrageous multifaceted nature and instability, and individuals are continually searching for a precise and successful approach to control stock trading. The exact expectation of stock cost could assume a significant job in helping speculators improve stock returns. The motivation behind this paper is to precisely foresee the pattern of stock costs, giving a reference model to the pattern of financial exchange and the following technique for stock value expectation, and offer some incentive reference for a look into the estimating model of securities exchange and speculators investment choice. Research using a hybrid model to anticipate the stock market will have a fundamental improvement that stood out from using a single model to forecast the same. The proposed model is a regression-based ensemble model where specialized technical indicators are used as input features to anticipate the 1-day future opening cost of individual stocks. In this paper, we had taken five regression-based machine learning algorithms (Lasso, SVR, RidgeCv, K-NN, random forest) to make ensemble-based hybrid models that are a combination of them. The combined ensemble models are Lasso + SVR + RidgeCv, Lasso + SVR + RandomForest, K-NN + SVR + RidgeCv, K-NN + SVR + RandomForest, K-NN + Lasso + RandomForest, Lasso + Random Forest + RidgeCv, Lasso + K-NN + RidgeCv, Lasso + K-NN + SVR. We have selected three stock indexes for our experiment, i.e., S&P 500, DJIA, HSI. During our research, we found that the combined predictive model "Lasso + SVR + RidgeCv" is a generalized model that can perform best on all three datasets. The proposed model gives the best MSE, MAE, RMSE values are 0.0308, 0.1348, 0.1756. Our proposed model can bring some direction and reference for some investors and market controllers. Our study offers down to earth experiences and possibly helpful headings for additional examination concerning how machine learning can be viably utilized for stock market investigation and expectation.

Comment on “Magnetic circular dichroism versus orbital magnetization”

In a recent article [Resta, Phys. Rev. Research 2, 023139 (2020)] it is argued, based on the dichroic sum rules derived from the modern theory of orbital magnetization, that the x-ray magnetic circular dichroism (XMCD) orbital magnetization sum rule is not providing an expectation value of the orbital angular momentum and of the orbital part of the magnetic moment, but a different quantity, also related to the breakdown of time-reversal invariance, but different. In this Comment, it is shown that this conclusion is incorrect, and that the XMCD sum rule, within its assumptions, delivers an essentially exact expectation value of the orbital angular momentum and of the orbital moment.

Machine Learning-Based Solar Power Energy Forecasting


 
 
 The expanding interest in energy is one of the main motivations behind the integration of solar energy into electric grids or networks. The exact expectation of solar oriented irradiance variety can improve the nature of administration. This coordination of solar-based vitality and exact expectations can help in better arranging and distributing of energy. Discovering vitality sources to fulfil the world’s developing interest is one of the general public’s major difficulties for the coming fifty years. In this research, two machine learning techniques utilized for hourly solar power forecasting are presented. The solar power prediction model becomes robust and efficient for solar power energy forecasting once the redundant information is removed from raw data, experimental data is transformed into a settled range, the best features selection method is chosen, four different weather profiles are made based on different weather conditions and the right time series machine learning algorithm is chosen.
 
 

Influence of near dry wirecut electrical discharge machining parameters on kerf width in Monel 400

Abstract This work explains the more refined and subtle analysis on one of the significant response parameters in kerf width upon machining Monel 400. Machining was done under near-dry ambiance with the support of the mathematical modeling technique of Response Surface Methodology (RSM) and the more sophisticated predictive computational modeling in an artificial neural network (ANN). Driving control elements considered for this WEDM process were pulse-on and off time (TON and TOFF), Voltage (V), Wire Feed (WF), Air inlet pressure and Water flow rate. The impact on the intermittent zone that prevails between the surface of the material in the spark zone and the wire during the process has not only being influenced by the control parameters but also by the dielectric medium. The implications of di-electric medium maintained at near dry conditions were given utmost importance and considerations in this investigation. The execution of the RSM and created ANN models are contrasted and trial consequences of Kerf Width for their adequacy. The examination demonstrates that ANN shows more exact expectation contrasted with the RSM models.

Decoherence of charge density waves in beam splitters for interacting quantum wires

Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special case of an intersection of topological edge states. We derive an effective impurity model which represents the edge-state intersection within Luttinger liquid theory at low energy. For Luttinger K = 1 / 2 , we compute the exact time-dependent expectation values of the charge density as well as the density-density correlation functions. In general a single incoming charge density wave packet will split into four outgoing wave packets with transmission and reflection coefficients depending on the strengths of the tunnelling processes between the wires at the junction. We find that when multiple charge density wave packets from different directions pass through the intersection at the same time, reflection and splitting of the packets depend on the relative phases of the waves. Active use of this phase-dependent splitting of wave packets may make Luttinger interferometry possible. We also find that coherent incident packets generally suffer partial decoherence from the intersection, with some of their initially coherent signal being transferred into correlated quantum noise. In an extreme case four incident coherent wave packets can be transformed entirely into density-density correlations, with the charge density itself having zero expectation value everywhere in the final state.

Accurate Sampling with Noisy Forces from Approximate Computing

In scientific computing, the acceleration of atomistic computer simulations by means of custom hardware is finding ever-growing application. A major limitation, however, is that the high efficiency in terms of performance and low power consumption entails the massive usage of low precision computing units. Here, based on the approximate computing paradigm, we present an algorithmic method to compensate for numerical inaccuracies due to low accuracy arithmetic operations rigorously, yet still obtaining exact expectation values using a properly modified Langevin-type equation.

Holography of massive M2-brane theory with discrete torsion

We investigate the gauge/gravity duality between the mathcal{N} = 6 mass-deformed ABJ theory with hbox {U}_k(N+l)times hbox {U}_{-k}(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1) times SO(4)/{mathbb Z}_ktimes SO(4)/{{mathbb {Z}}}_k isometry and the discrete torsion l. For chiral primary operators with conformal dimensions Delta =1,2, we obtain the exact vacuum expectation values using the holographic method in 11-dimensional supergravity and show that the results depend on the shapes of droplet pictures in LLM geometries. The frac{l}{sqrt{N}} contributions from the discrete torsion l for several simple droplet pictures in the large N limit are determined in holographic vacuum expectation values. We also explore the effects of the orbifolding {{mathbb {Z}}}_k and the asymptotic discrete torsion l, on the gauge/gravity duality dictionary and on the nature of the asymptotic limits of the LLM geometries.