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A stochastic MPEC approach for grid tariff design with demand-side flexibility

ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2023年第3期14卷 707-729页

作者： Askeland, Magnus Burandt, Thorsten Gabriel, Steven A. Energy Systems SINTEF Energy Research Trondheim Norway Department of Electric Power Engineering Norwegian University of Science and Technology Trondheim Norway Workgroup for Infrastructure Policy Technical University of Berlin Berlin Germany The Energy Transportation Environment Department German Institute for Economic Research (DIW Berlin) Berlin Germany Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim Norway Department of Mechanical Engineering Applied Math and Statistics Scientific Computation Program University of Maryland College Park MD USA

As the end-users increasingly can provide flexibility to the power system, it is important to consider how this flexibility can be activated as a resource for the grid. Electricity network tariffs is one option that can be used to activate this flexibility. Therefore, by designing efficient grid tariffs, it might be possible to reduce the total costs in the power system by incentivizing a change in consumption patterns. This paper provides a methodology for optimal grid tariff design under decentralized decision-making and uncertainty in demand, power prices, and renewable generation. A bilevel model is formulated to adequately describe the interaction between the end-users and a distribution system operator. In addition, a centralized decision-making model is provided for benchmarking purposes. The bilevel model is reformulated as a mixed-integer linear problem solvable by branch-and-cut techniques. Results based on both deterministic and stochastic settings are presented and discussed. The findings suggest how electricity grid tariffs should be designed to provide an efficient price signal for reducing aggregate network peaks.

关键词： Bilevel problem Grid tariffs mathematical program with equilibrium constraints (MPEC) Uncertainty

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Principal Curvatures Estimation with Applications to Single Cell Data

Principal Curvatures Estimation with Applications to Single ...

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2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025

作者： Zhang, Yanlei Mezrag, Lydia Sun, Xingzhi Xu, Charles Macdonald, Kincaid Bhaskar, Dhananjay Krishnaswamy, Smita Wolf, Guy Rieck, Bastian Université de Montréal Dept. of Math. & Stat Canada Mila - Quebec AI Institute MontréalQC Canada Yale University Dept. of Comp. Sci. United States Dept. of Genetics United States Applied Mathematics Program New HavenCT United States Université de Fribourg Department of Informatics FR Fribourg Switzerland Helmholtz Zentrum München Institute of AI for Health BY Munich Germany

ISBN: (纸本)9798350368741

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower dimensional manifold. This allows to study the geometry of point clouds by extracting meaningful descriptors like curvature. In this work, we will present Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating various notions of intrinsic curvature on data manifolds, in particular principal curvatures for surfaces. The model relies on local PCA to estimate the tangent spaces. The evaluation of AdaL-PCA on sampled surfaces shows state-of-the-art results. Combined with a PHATE embedding, the model applied to single-cell RNA sequencing data allows us to identify key variations in the cellular differentiation. © 2025 IEEE.

关键词： Gaussian curvature Principal curvature principal directions single-cell

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A measurement of the cosmic expansion within our lifetime

arXiv

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arXiv 2021年

作者： Melia, Fulvio Department of Physics Applied Math Program The University of Arizona TucsonAZ85721 United States

The most exciting future observation in cosmology will feature a monitoring of the cosmic expansion in real time, unlike anything that has ever been attempted before. This campaign will uncover crucial physical properties of the various constituents in the Universe, and perhaps answer a simpler question concerning whether or not the cosmic expansion is even accelerating. An unambiguous yes/no response to this query will significantly impact cosmology, of course, but also the standard model of particle physics. Here, we discuss-in a straightforward way-how to understand the so-called 'redshift drift' sought by this campaign, and why its measurement will help us refine the standard-model parameters if the answer is 'yes.' A 'no' answer, on the other hand, could be more revolutionary, in the sense that it might provide a resolution of several long-standing problems and inconsistencies in our current cosmological models. An outcome of zero redshift drift, for example, would obviate the need for a cosmological constant and render inflation completely redundant. © 2021, CC BY.

关键词： Expansion

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Modeling functional cell types in spike train data

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PLoS Computational Biology 2023年第10 October期19卷 e1011509-e1011509页

作者： Zdeblick, Daniel N. Shea-Brown, Eric T. Witten, Daniela M. Buice, Michael A. Department of Electrical and Computer Engineering University of Washington SeattleWA United States Department of Applied Math University of Washington SeattleWA United States MindScope Program Allen Institute SeattleWA United States Department of Statistics and Biostatistics University of Washington SeattleWA United States

A major goal of computational neuroscience is to build accurate models of the activity of neurons that can be used to interpret their function in circuits. Here, we explore using functional cell types to refine single-cell models by grouping them into functionally relevant classes. Formally, we define a hierarchical generative model for cell types, single-cell parameters, and neural responses, and then derive an expectation-maximization algorithm with variational inference that maximizes the likelihood of the neural recordings. We apply this "simultaneous" method to estimate cell types and fit single-cell models from simulated data, and find that it accurately recovers the ground truth parameters. We then apply our approach to in vitro neural recordings from neurons in mouse primary visual cortex, and find that it yields improved prediction of single-cell activity. We demonstrate that the discovered cell-type clusters are well separated and generalizable, and thus amenable to interpretation. We then compare discovered cluster memberships with locational, morphological, and transcriptomic data. Our findings reveal the potential to improve models of neural responses by explicitly allowing for shared functional properties across neurons. Copyright: © 2023 Zdeblick et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

关键词： Neurons

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The anomalous 21-cm absorption at high redshifts

arXiv

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arXiv 2021年

作者： Melia, Fulvio Department of Physics Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

The EDGES collaboration has reported the detection of a global 21-cm signal with a plateau centered at 76 MHz (i.e., redshift 17.2), with an amplitude of 500+200−500 mK. This anomalous measurement does not comport with standard cosmology, which can only accommodate an amplitude . 230 mK. Nevertheless, the line profile’s redshift range (15 . z . 20) suggests a possible link to Pop III star formation and an implied evolution out of the ‘dark ages.’ Given this tension with the standard model, we here examine whether the observed 21-cm signal is instead consistent with the results of recent modeling based on the alternative Friedmann-Lemaître-Robertson-Walker cosmology known as the Rh = ct universe, showing that—in this model—the CMB radiation might have been rethermalized by dust ejected into the IGM by the first-generation stars at redshift z ∼ 16. We find that the requirements for this process to have occurred would have self-consistently established an equilibrium spin temperature Ts ≈ 3.4 K in the neutral hydrogen, via the irradiation of the IGM by deep penetrating X-rays emitted at the termination shocks of Pop III supernova remnants. Such a dust scenario has been strongly ruled out for the standard model, so the spin temperature (∼ 3.3 K) inferred from the 21-cm absorption feature appears to be much more consistent with the Rh = ct profile than that implied by ΛCDM, for which adiabatic cooling would have established a spin temperature Ts(z = 17.2) ∼ 6 K. © 2021, CC BY.

关键词： Cosmology

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Classicalization of Quantum Fluctuations at the Planck Scale in the Rh=ct Universe

Research Square

引用

Research Square 2021年

作者： Melia, Fulvio Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

The quantum to classical transition of fluctuations in the early universe is still not completely understood. Some headway has been made incorporating the effects of decoherence and the squeezing of states, though the methods and procedures continue to be challenged. But new developments in the analysis of the most recent Planck data suggest that the primordial power spectrum has a cutoff associated with the very first quantum fluctuation to have emerged into the semi-classical universe from the Planck domain at about the Planck time. In this paper, we examine the implications of this result on the question of classicalization, and demonstrate that the birth of quantum fluctuations at the Planck scale would have been a ‘process’ supplanting the need for a ‘measurement’ in quantum mechanics. Emerging with a single wavenumber, these fluctuations would have avoided the interference between different degrees of freedom in a superposed state. Moreover, the implied scalar-field potential had an equation-of-state consistent with the zero active mass condition in general relativity, allowing the quantum fluctuations to emerge in their ground state with a time-independent frequency. They were therefore effectively quantum harmonic oscillators with classical correlations in phase space from the very beginning. © 2021, CC BY.

关键词： Degrees of freedom (mechanics)

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Thermodynamics of the Rh = ct Universe: A simplification of cosmic entropy

arXiv

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arXiv 2021年

作者： Melia, Fulvio Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

In the standard model of cosmology, the Universe began its expansion with an anomalously low entropy, which then grew dramatically to much larger values consistent with the physical conditions at decoupling, roughly 380,000 years after the Big Bang. There does not appear to be a viable explanation for this ‘unnatural’ history, other than via the generalized second law of thermodynamics (GSL), in which the entropy of the bulk, Sbulk, is combined with the entropy of the apparent (or gravitational) horizon, Sh. This is not completely satisfactory either, however, since this approach seems to require an inexplicable equilibrium between the bulk and horizon temperatures. In this paper, we explore the thermodynamics of an alternative cosmology known as the Rh = ct universe, which has thus far been highly successful in resolving many other problems or inconsistencies in ΛCDM. We find that Sbulk is constant in this model, eliminating the so-called initial entropy problem simply and elegantly. The GSL may still be relevant, however, principally in selecting the arrow of time, given that Sh ∝ t2 in this model. © 2021, CC BY.

关键词： Entropy

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The origin of rest-mass energy

arXiv

引用

arXiv 2021年

作者： Melia, Fulvio Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

Today we have a solid, if incomplete, physical picture of how inertia is created in the standard model. We know that most of the visible baryonic 'mass' in the Universe is due to gluonic back-reaction on accelerated quarks, the latter of which attribute their own inertia to a coupling with the Higgs field-a process that elegantly and self-consistently also assigns inertia to several other particles. But we have never had a physically viable explanation for the origin of rest-mass energy, in spite of many attempts at understanding it towards the end of the nineteenth century, culminating with Einstein's own landmark contribution in his Annus Mirabilis. Here, we introduce to this discussion some of the insights we have garnered from the latest cosmological observations and theoretical modeling to calculate our gravitational binding energy with that portion of the Universe to which we are causally connected, and demonstrate that this energy is indeed equal to mc2 when the inertia m is viewed as a surrogate for gravitational mass. © 2021, CC BY.

关键词： Binding energy

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Classicalization of quantum fluctuations at the Planck scale in the Rh = CT universe

arXiv

引用

arXiv 2021年

作者： Melia, Fulvio Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

The quantum to classical transition of fluctuations in the early universe is still not completely understood. Some headway has been made incorporating the effects of decoherence and the squeezing of states, though the methods and procedures continue to be challenged. But new developments in the analysis of the most recent Planck data suggest that the primordial power spectrum has a cutoff associated with the very first quantum fluctuation to have emerged into the semi-classical universe from the Planck domain at about the Planck time. In this paper, we examine the implications of this result on the question of classicalization, and demonstrate that the birth of quantum fluctuations at the Planck scale would have been a 'process' supplanting the need for a 'measurement' in quantum mechanics. Emerging with a single wavenumber, these fluctuations would have avoided the interference between different degrees of freedom in a superposed state. Moreover, the implied scalar-field potential had an equation-of-state consistent with the zero active mass condition in general relativity, allowing the quantum fluctuations to emerge in their ground state with a time-independent frequency. They were therefore effectively quantum harmonic oscillators with classical correlations in phase space from the very beginning. © 2021, CC BY.

关键词： Degrees of freedom (mechanics)

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HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

arXiv

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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

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