arXiv subjects

T. Mei

Publications and source records attributed to T. Mei.

16 recordsLinked to original sources

arXiv2022

Evaluation of data imputation strategies in complex, deeply-phenotyped data sets: the case of the EU-AIMS Longitudinal European Autism Project

An increasing number of large-scale multi-modal research initiatives has been conducted in the typically developing population, as well as in psychiatric cohorts. Missing data is a common problem in such datasets due to the difficulty of assessing multiple measures on a large number of participants. The consequences of missing data accumulate when researchers aim to explore relationships between multiple measures. Here we aim to evaluate different imputation strategies to fill in missing values in clinical data from a large (total N=764) and deeply characterised (i.e. range of clinical and cognitive instruments administered) sample of N=453 autistic individuals and N=311 control individuals recruited as part of the EU-AIMS Longitudinal European Autism Project (LEAP) consortium. In particular we consider a total of 160 clinical measures divided in 15 overlapping subsets of participants. We use two simple but common univariate strategies, mean and median imputation, as well as a Round Robin regression approach involving four independent multivariate regression models including a linear model, Bayesian Ridge regression, as well as several non-linear models, Decision Trees, Extra Trees and K-Neighbours regression. We evaluate the models using the traditional mean square error towards removed available data, and consider in addition the KL divergence between the observed and the imputed distributions. We show that all of the multivariate approaches tested provide a substantial improvement compared to typical univariate approaches. Further, our analyses reveal that across all 15 data-subsets tested, an Extra Trees regression approach provided the best global results. This allows the selection of a unique model to impute missing data for the LEAP project and deliver a fixed set of imputed clinical data to be used by researchers working with the LEAP dataset in the future.

cs.LG↗

arXiv2020

Development, Demonstration, and Validation of Data-driven Compact Diode Models for Circuit Simulation and Analysis

Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not trivial and may require redevelopment from scratch. Machine Learning (ML) techniques have the potential to automate and significantly speed up the development of compact models. In addition, ML provides a range of modeling options that can be used to develop hierarchies of compact models tailored to specific circuit design stages. In this paper, we explore three such options: (1) table-based interpolation, (2)Generalized Moving Least-Squares, and (3) feed-forward Deep Neural Networks, to develop compact models for a p-n junction diode. We evaluate the performance of these "data-driven" compact models by (1) comparing their voltage-current characteristics against laboratory data, and (2) building a bridge rectifier circuit using these devices, predicting the circuit's behavior using SPICE-like circuit simulations, and then comparing these predictions against laboratory measurements of the same circuit.

cs.LG↗

arXiv2016

Nonreciprocity light propagation in coupled microcavities system beyond weak-excitation approximation

We propose an alternative scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time (\textrm{PT}) system (i.e., active-passive coupled cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The giant optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.

quant-ph↗

arXiv2011

A kind of model of quantum electrodynamics with nonlocal interaction

We present a kind of model of quantum electrodynamics with nonlocal interaction, all the action and the equations of motion of charged particle and electromagnetic field are given. The main characteristics of the theory are: the model obeys the action principle; free charged particle and free electromagnetic field obey the Dirac equation and the Maxwell equation of free fields, respectively; for the case of interaction, both the equations of motion of charged particle and electromagnetic field lead to the normal current conservation naturally; the theory is Lorentz invariant and gauge invariant, and returns to the conventional local QED under appropriate limit conditions. Taking advantage of the Yang-Feldman equations and the Lehmann-Symanzik- Zimmermann formalism, we establish the corresponding quantum theory.

hep-th↗

arXiv2010

General Relativity as a fully singular Lagrange system

We present some gauge conditions to eliminate all second time derivative terms in the vierbein forms of the ten Einstein equations of general relativity; at the same time, we present the corresponding Lagrangian in which there is not any quadratic term of first time derivative that can leads to those vierbein forms of the Einstein equations without second time derivative term by the corresponding Euler-Lagrange equations. General relativity thus becomes a fully singular Lagrange system.

gr-qc↗

arXiv2010

Undecidable propositions with Diophantine form arisen from every axiom and every theorem of Peano Arithmetic

Based on the MRDP theorem, we introduce the ideas of the proof equation of a formula and universal proof equation of Peano Arithmetic (PA); and then, combining universal proof equation and Gödel's Second Incompleteness Theorem, it is proved that, if PA is consistent, then for every axiom and every theorem of PA, we can construct a corresponding undecidable proposition with Diophantine form. Finally, we present an approach that transforms seeking a proof of a mathematical (set theoretical, number theoretical, algebraic, geometrical, topological, etc) proposition into solving a Diophantine equation.

math.LO↗

arXiv2009

Negative kinetic energy term of general relativity and its removing

We first present a new Lagrangian of general relativity, which can be divided into kinetic energy term and potential energy term. Taking advantage of vierbein formalism, we reduce the kinetic energy term to a sum of five positive terms and one negative term. Some gauge conditions removing the negative kinetic energy term are discussed. Finally, we present a Lagrangian that only include positive kinetic energy terms. To remove the negative kinetic energy term leads to a new field equation of general relativity in which there are at least five equations of constraint and at most five dynamical equations, this characteristic is different from the normal Einstein field equation in which there are four equations of constraint and six dynamical equations.

gr-qc↗

arXiv2008

A theory of quantum electrodynamics with nonlocal interaction

In this paper, we present a theory of quantum electrodynamics with nonlocal interaction, a main characteristic of the theory is that a charged particle situated x^{mu} interacts with electromagnetic field situated y^{mu}, where x^{mu}=y^{mu}+aA^{mu}, A^{mu} reads electromagnetic 4-potential, a is a constant. All the action, the equations of motion of charged particle and electromagnetic field are given. For the case of free fields, charged particle and electromagnetic field obey the Dirac equation and the Maxwell equation of free fields, respectively; for the case with interaction, both the equations of motion of charged particle and electromagnetic field lead to current conservation j^{mu}_{,mu}=0 naturally. The theory is Lorentz invariant and gauge invariant under a generalized gauge transformation, the generalized gauge transformation can guarantee that the temporal gauge condition A^{0} holds or the Lorentz gauge condition A^{mu}_{,mu}=0 holds, respectively. The theory returns to the current QED when a=0. Finally, taking advantage of the Lehmann-Symanzik-Zimmermann approach, we establish the corresponding quantum theory.

hep-th↗

arXiv2008

On the calculation rule of probability of relativistic free particle in quantum mechanics

As is well known, in quantum mechanics, the calculation rule of the probability that an eigen-value a_n is observed when the physical quantity A is measured for a state described by the state vector |> is P(a_n)=<|A_n> . However, in Ref.[1], based on strict logical reasoning and mathematical calculation, it has been pointed out, replacing <|A_n> , one should use a new rule to calculate P(a_n) for particle satisfying the Dirac equation. In this paper, we first state some results given by Ref.[1]. And then, we present a proof for the new calculation rule of probability according to Dirac sea of negative energy particles, hole theory and the principle "the vacuum is not observable". Finally, we discuss simply the case of particle satisfying the Klein-Gordon equation.

physics.gen-ph↗

arXiv2008

On spherically symmetric metric satisfying the positive kinetic energy coordinate condition

Generally speaking, there is a negative kinetic energy term in the Lagrangian of the Einstein-Hilbert action of general relativity; On the other hand, the negative kinetic energy term can be vanished by designating a special coordinate system. For general spherically symmetric metric, the question that seeking special coordinate system that satisfies the positive kinetic energy coordinate condition is referred to solving a linear first-order partial differential equation. And then, we present a metric corresponding to the Reissner-Nordstrom solution that satisfies the positive kinetic energy coordinate condition. Finally, we discuss simply the case of the Tolman metric.

gr-qc↗

arXiv2007

On the vierbein formalism of general relativity

Both the Einstein-Hilbert action and the Einstein equations are discussed under the absolute vierbein formalism. Taking advantage of this form, we prove that the "kinetic energy" term, i.e., the quadratic term of time derivative term, in the Lagrangian of the Einstein-Hilbert action is non-positive definitive. And then, we present two groups of coordinate conditions that lead to positive definitive kinetic energy term in the Lagrangian, as well as the corresponding actions with positive definitive kinetic energy term, respectively. Based on the ADM decomposition, the Hamiltonian representation and canonical quantization of general relativity taking advantage of the actions with positive definitive kinetic energy term are discussed; especially, the Hamiltonian constraints with positive definitive kinetic energy term are given, respectively. Finally, we present a group of gauge conditions such that there is not any second time derivative term in the ten Einstein equations.

gr-qc↗

arXiv2007

An action with positive kinetic energy term for general relativity

At first, we state some results in arXiv: 0707.2639, and then, using a positive kinetic energy coordinate condition given by arXiv: 0707.2639, we present an action with positive kinetic energy term for general relativity. Based on this action, the corresponding theory of canonical quantization is discussed.

gr-qc↗

arXiv2007

Undecidable proposition in PA and Diophantine equation

Based on the MRDP theorem concerning the Hilbert tenth problem, there is a corresponding Diophantine equation called proof equation for every formula of the First-order Peano Arithmetic (PA). A formula is provable in PA, if and only if the corresponding proof equation has solution. Based on proof equation, some famous sentences, e.g., the Godel sentence, the Rosser sentence and the Henkin sentence, can be expressed by the form of Diophantine equation. It is proved that for every axiom and theorem in the PA, we can construct actually a corresponding Diophantine equation, for which we know that it has no solution, but this fact cannot be proved in the PA. This means that, for every axiom and theorem in the PA, we can construct actually a corresponding undecidable proposition. Finally, generalizing the idea of proof equation to any mathematical (set theoretical, number theoretical, algebraic, geometrical, topological, et al) proposition, a project translating the task seeking a proof of the mathematical proposition into solving a corresponding Diophantine equation is discussed.

math.LO↗

arXiv2006

A New Variable in General Relativity and Its Applications for Classic and Quantum Gravity

A new variable in the Riemannian geometry is introduced by the tetrad and the Ricci's coefficients of rotation, the characters of curve of the Riemannian geometry are determined completely by the new variable; for general relativity, all the Einstein-Hilbert action, the Einstein equation in general relativity and the Dirac equation in curved spacetime can be expressed by the new variable, and, further, as well the action of the theory on the interaction of gravitational, electromagnetic and spinor field (TGESF). All the characters of transformations of the new variable, the Einstein-Hilbert action and the action of TGESF under the general coordinate transformations and the local Lorentz transformations are discussed, respectively. After presenting the method of introduction of gravitational field in terms of the principle of gauge invariance based on the Dirac equation, and the ten constraint conditions for the tetrad are given, the vacuum-vacuum transition amplitude with the Faddeev-Popov ghost and the terms of external sources of the pure gravitational field is presented; finally, as well that of TGESF.

gr-qc↗

arXiv2006

On isotropic metric of Schwarzschild solution of Einstein equation

The known static isotropic metric of Schwarzschild solution of Einstein equation cannot cover with the range of r<2MG, a new isotropic metric of Schwarzschild solution is obtained. The new isotropic metric has the characters: (1) It is dynamic and periodic. (2) It has infinite singularities of the spacetime. (3) It cannot cover with the range of 0<r<r0; On the other hand, r0 can be small discretionarily. (4) It seemed as if the range of negative r could be unavoidable, although this range is meaningless for the Schwarzschild metric.

gr-qc↗

arXiv2006

The Berry-like Sentence in the First-order Peano Arithmetic System with the Operation of Factorial

A first-order Peano Arithmetical system with the operation of factorial (PAF) is introduced. For any formula A(x) with a free variable x in PAF, we define a corresponding B-formula which means that there exists unique number that is smallest in all natural numbers satisfying the formula A(x) that satisfies the B-formula if A(x) is satisfiable. And then, we construct a formula which means that "there exists x, for any B-formula whose Godel code is smaller than a constant a, x does not satisfy this B-formula, and x is the smallest in those numbers that have such character." However, the constructed formula itself is a B-formula and its Godel code is smaller than a. Thus, it is a version in PAF of the Berry sentence "The smallest positive integer not nameable in under eleven words" that itself is in only ten words.

math.LO↗