Project description:Simulation-based inference for partially observed stochastic dynamic models is currently receiving much attention due to the fact that direct computation of the likelihood is not possible in many practical situations. Iterated filtering methodologies enable maximization of the likelihood function using simulation-based sequential Monte Carlo filters. Doucet et al. (2013) developed an approximation for the first and second derivatives of the log likelihood via simulation-based sequential Monte Carlo smoothing and proved that the approximation has some attractive theoretical properties. We investigated an iterated smoothing algorithm carrying out likelihood maximization using these derivative approximations. Further, we developed a new iterated smoothing algorithm, using a modification of these derivative estimates, for which we establish both theoretical results and effective practical performance. On benchmark computational challenges, this method beat the first-order iterated filtering algorithm. The method's performance was comparable to a recently developed iterated filtering algorithm based on an iterated Bayes map. Our iterated smoothing algorithm and its theoretical justification provide new directions for future developments in simulation-based inference for latent variable models such as partially observed Markov process models.
Project description:Luminance variations are ambiguous: they can signal changes in surface reflectance or changes in illumination. Layer decomposition-the process of distinguishing between reflectance and illumination changes-is supported by a range of secondary cues including colour and texture. For an illuminated corrugated, textured surface the shading pattern comprises modulations of luminance (first order, LM) and local luminance amplitude (second-order, AM). The phase relationship between these two signals enables layer decomposition, predicts the perception of reflectance and illumination changes, and has been modelled based on early, fast, feed-forward visual processing (Schofield et al., 2010). However, while inexperienced viewers appreciate this scission at long presentation times, they cannot do so for short presentation durations (250 ms). This might suggest the action of slower, higher-level mechanisms. Here we consider how training attenuates this delay, and whether the resultant learning occurs at a perceptual level. We trained observers to discriminate the components of plaid stimuli that mixed in-phase and anti-phase LM/AM signals over a period of 5 days. After training, the strength of the AM signal needed to differentiate the plaid components fell dramatically, indicating learning. We tested for transfer of learning using stimuli with different spatial frequencies, in-plane orientations, and acutely angled plaids. We report that learning transfers only partially when the stimuli are changed, suggesting that benefits accrue from tuning specific mechanisms, rather than general interpretative processes. We suggest that the mechanisms which support layer decomposition using second-order cues are relatively early, and not inherently slow.
Project description:We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.
Project description:In the field of asset allocation, how to balance the returns of an investment portfolio and its fluctuations is the core issue. Capital asset pricing model, arbitrage pricing theory, and Fama-French three-factor model were used to quantify the price of individual stocks and portfolios. Based on the second-order stochastic dominance rule, the higher moments of return series, the Shannon entropy, and some other actual investment constraints, we construct a multiconstraint portfolio optimization model, aiming at comprehensively weighting the returns and risk of portfolios rather than blindly maximizing its returns. Furthermore, the whale optimization algorithm based on FTSE100 index data is used to optimize the above multiconstraint portfolio optimization model, which significantly improves the rate of return of the simple diversified buy-and-hold strategy or the FTSE100 index. Furthermore, extensive experiments validate the superiority of the whale optimization algorithm over the other four swarm intelligence optimization algorithms (gray wolf optimizer, fruit fly optimization algorithm, particle swarm optimization, and firefly algorithm) through various indicators of the results, especially under harsh constraints.
Project description:Because the traditional Cholesky decomposition algorithm still has some problems such as computational complexity and scattered structure among matrices when solving the GNSS ambiguity, it is the key problem to further improve the computational efficiency of the least squares ambiguity reduction correlation process in the carrier phase integer ambiguity solution. But the traditional matrix decomposition calculation is more complex and time-consuming, to improve the efficiency of the matrix decomposition, in this paper, the decomposition process of traditional matrix elements is divided into two steps: multiplication update and column reduction of square root calculation. The column reduction step is used to perform square root calculation and column division calculation, while the update step is used for the update task of multiplication. Based on the above ideas, the existing Cholesky decomposition algorithm is improved, and a column oriented Cholesky (C-Cholesky) algorithm is proposed to further improve the efficiency of matrix decomposition, so as to shorten the calculation time of integer ambiguity reduction correlation. The results show that this method is effective and superior, and can improve the data processing efficiency by about 12.34% on average without changing the integer ambiguity accuracy of the traditional Cholesky algorithm.
Project description:In the "footsteps illusion", light and dark squares travel at constant speed across black and white stripes. The squares appear to move faster and slower as their contrast against the stripes varies. We now demonstrate some second-order footsteps illusions, in which all edges are defined by colors or textures-even though luminance-based neural motion detectors are blind to such edges.
Project description:Agents make predictions based on similar past cases, while also learning the relative importance of various attributes in judging similarity. We ask whether the resulting "empirically optimal similarity function" (EOSF) is unique and how easy it is to find it. We show that with many observations and few relevant variables, uniqueness holds. By contrast, when there are many variables relative to observations, nonuniqueness is the rule, and finding the EOSF is computationally hard. The results are interpreted as providing conditions under which rational agents who have access to the same observations are likely to converge on the same predictions and conditions under which they may entertain different probabilistic beliefs.
Project description:Electron-phonon (e-ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e-ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-range e-ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles.
Project description:Second-order nonlinear spectroscopy has proven to be a powerful tool in elucidating key chemical and structural characteristics at a variety of interfaces. However, the presence of interfacial potentials may lead to complications regarding the interpretation of second harmonic and vibrational sum frequency generation responses from charged interfaces due to mixing of absorptive and dispersive contributions. Here, we examine by means of mathematical modeling how this interaction influences second-order spectral lineshapes. We discuss our findings in the context of reported nonlinear optical spectra obtained from charged water/air and solid/liquid interfaces and demonstrate the importance of accounting for the interfacial potential-dependent χ (3) term in interpreting lineshapes when seeking molecular information from charged interfaces using second-order spectroscopy.