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Robust utility maximization with intractable claims

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arXiv 2023年

作者： Li, Yunhong Xu, Zuo Quan Zhou, Xun Yu Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon Hong Kong Department of Industrial Engineering and Operations Research The Data Science Institute Columbia University New YorkNY10027 United States

We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution, hence an "intractable claim". In view of the lack of necessary information about the claim, we consider a robust formulation to maximize her utility in the worst scenario. We apply the quantile formulation to solve the problem, expressing the quantile function of the optimal terminal investment income as the solution of certain variational inequalities of ordinary differential equations and obtaining the resulting optimal trading strategy. In the case of an exponential utility, the problem reduces to a (non-robust) rank-dependent utility maximization with probability distortion whose solution is available in the literature. The results can also be used to determine the utility indifference price of the intractable *** Codes 91B28, 91G10, 35Q91 Copyright © 2023, The Authors. All rights reserved.

关键词： Investments

Laser Synthesis of Linear Carbon Structures for Nanophotonics

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Laser Synthesis of Linear Carbon Structures for Nanophotonic...

Progress in Electromagnetic Research Symposium (PIERS)

作者： A. V. Osipov V. D. Samyshkin A. S. Abramov D. S. Bodunov A. V. Povolotskiy E. S. Sedov A. O. Kucherik Department of Physics and Applied Mathematics Stoletov Vladimir State University Russia Institute of Chemistry St. Petersburg State University Russia School of Science Westlake University Hangzhou Zhejiang China Institute of Natural Sciences Westlake Institute for Advanced Study Hangzhou Zhejiang China

ISBN: (数字)9798350375909

ISBN: (纸本)9798350375916

Here we study stable elongated carbon chains synthesized by the laser fragmentation technique in a colloidal solution. The mechanical stabilization of carbyne is achieved due to the electron bonding of carbon chains to gold nanoparticles. The high degree of alignment of the gold-terminated carbyne chains results in strongly anisotropic light absorption characterized by a distinctive cosine dependence on the angle between the carbyne molecule and polarization plane of the excitation.

关键词： Nanoparticles Resistance Radiation effects Polarization Gold Absorption Ultraviolet sources

Applying Kerr Squeezed Light to Interferometry

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Applying Kerr Squeezed Light to Interferometry

2023 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2023

作者： Kalinin, Nikolay Dirmeier, Thomas Sorokin, Arseny A. Anashkina, Elena A. Sánchez-Soto, Luis L. Corney, Joel F. Leuchs, Gerd Andrianov, Alexey V. Max Planck Institute for the Science of Light Erlangen91058 Germany Physik Department Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen91058 Germany Nexus for Quantum Technologies University of Ottawa OttawaONK1N 6N5 Canada Nonlinear Dynamics and Optics Division Institute of Applied Physics The Russian Academy of Sciences Nizhny Novgorod603950 Russia Advanced School of General and Applied Physics Lobachevsky State University of Nizhny Novgorod Nizhny Novgorod603022 Russia Departamento de Óptica Facultad de Física Universidad Complutense Madrid28040 Spain School of Mathematics and Physics University of Queensland BrisbaneQLD4072 Australia

ISBN: (纸本)9798350345995

One of the most promising applications for squeezed light is interferometry beyond the shot-noise limit (SNL). To date, only squeezed light generated by parametric down-conversion has been used to improve interferometer sensitivity. Remarkable results have been achieved with this approach, including applications to large-scale gravitational wave detectors. On the other hand, there exists a potentially more robust way to generate squeezed light, that is, using the optical Kerr effect. It occurs almost for free in optical fibers and requires no phase matching. However, no interferometer sensitivity enhancement has been demonstrated so far using this method. One of the reasons for that is that the uncertainty distribution of a Kerr-squeezed state in phase space is tilted with respect to the amplitude or phase quadratures. Additional obstacles include Raman and guided acoustic wave Brillouin scattering in fibers. © 2023 IEEE.

关键词： Interferometers

Integrability of polynomial vector fields and a dual problem

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arXiv 2024年

作者： Petek, Tatjana Romanovski, Valery G. Faculty of Electrical Engineering and Computer Science University of Maribor Koroska cesta 46 MariborSI-2000 Slovenia Institute of Mathematics Physics and Mechanics Jadranska 19 LjubljanaSI-1000 Slovenia Faculty of Natural Science and Mathematics University of Maribor Koroska cesta 160 MariborSI-2000 Slovenia Center for Applied Mathematics and Theoretical Physics Mladinska 3 MariborSI-2000 Slovenia

We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality the case of quadratic vector fields is considered in detail. © 2024, CC BY.

关键词： Choquet integral

Any-dimensional equivariant neural networks

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arXiv 2023年

作者： Levin, Eitan Díaz, Mateo Department of Computing and Mathematical Sciences Caltech PasadenaCA91125 United States Department of Applied Mathematics and Statistics The Mathematical Institute for Data Science Johns Hopkins University BaltimoreMD21218 United States

Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings, the unknown mapping takes inputs in any dimension;examples include graph parameters defined on graphs of any size and physics quantities defined on an arbitrary number of particles. We leverage a newly-discovered phenomenon in algebraic topology, called representation stability, to define equivariant neural networks that can be trained with data in a fixed dimension and then extended to accept inputs in any dimension. Our approach is black-box and user-friendly, requiring only the network architecture and the groups for equivariance, and can be combined with any training procedure. We provide a simple open-source implementation of our methods and offer preliminary numerical experiments. Copyright © 2023, The Authors. All rights reserved.

关键词： Network architecture

Evolutionary dynamics in non-Markovian models of microbial populations

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Physical Review E 2023年第3期108卷 034402-034402页

作者： Farshid Jafarpour Ethan Levien Ariel Amir Institute for Theoretical Physics Utrecht University 3584 CC Utrecht The Netherlands Mathematics Department Dartmouth College Hanover New Hampshire 03755 USA Department of Complex Systems Faculty of Physics The Weizmann Institute of Science Rehovot 7610001 Israel John A. Paulson School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA

In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the Euler-Lotka equation.

关键词： Population genetics Microbial multicellular systems Populations

Intermolecular Charge Transfer Induced Fragmentation of Formic Acid Dimers

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Physical Review Letters 2023年第23期130卷 233001-233001页

作者： Jiaqi Zhou Shaokui Jia Xiaoqing Hu Enliang Wang Xiaorui Xue Yong Wu Jianguo Wang Alexander Dorn Xueguang Ren School of Physics Xi’an Jiaotong University Xi’an 710049 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics University of Science and Technology of China Hefei 230026 China Max-Planck-Institut für Kernphysik Saupfercheckweg 1 69117 Heidelberg Germany

We investigate the intermolecular nonradiative charge transfer process in a double hydrogen-bonded formic acid (FA) dimer, initiated by electron-collision induced double ionization of one FA molecule. Through fragment ions and electron coincident momentum measurements and ab initio calculations, we obtain direct evidence that electron transfer from the neighboring FA molecule to fill one of the two vacancies occurs by a potential energy curve crossing of FA+++FA with FA++FA+* curves, forming an electronic excited state of dicationic dimers. This process causes the breaking of two hydrogen bonds and subsequently the cleavage of C─H and C─O covalent bonds in the dimers, which is expected to be a general phenomenon occurring in molecular complexes and can have important implications for radiation damage to biological matter.

关键词： Atomic & molecular structure Electronic excitation & ionization Interatomic & molecular potentials Molecular dynamics

Cache Blocking of Distributed-Memory Parallel Matrix Power Kernels

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arXiv 2024年

作者： Lacey, Dane Alappat, Christie Lange, Florian Hager, Georg Fehske, Holger Wellein, Gerhard Friedrich-Alexander-Universität Erlangen-Nürnberg Germany Institute of Physics University of Greifswald Germany Department of Computer Science Friedrich-Alexander-Universität Erlangen-Nürnberg Germany Delft Institute of Applied Mathematics Delft University of Technology Netherlands

Sparse matrix-vector products (SpMVs) are a bottleneck in many scientific codes. Due to the heavy strain on the main memory interface from loading the sparse matrix and the possibly irregular memory access pattern, SpMV typically exhibits low arithmetic intensity. Repeating these products multiple times with the same matrix is required in many algorithms. This so-called matrix power kernel (MPK) provides an opportunity for data reuse since the same matrix data is loaded from main memory multiple times, an opportunity that has only recently been exploited successfully with the Recursive Algebraic Coloring Engine (RACE). Using RACE, one considers a graph based formulation of the SpMV and employs s level-based implementation of SpMV for reuse of relevant matrix data. However, the underlying data dependencies have restricted the use of this concept to shared memory parallelization and thus to single compute nodes. Enabling cache blocking for distributed-memory parallelization of MPK is challenging due to the need for explicit communication and synchronization of data in neighboring levels. In this work, we propose and implement a flexible method that interleaves the cache-blocking capabilities of RACE with an MPI communication scheme that fulfills all data dependencies among processes. Compared to a "traditional" distributed memory parallel MPK, our new Distributed Level-Blocked MPK yields substantial speed-ups on modern Intel and AMD architectures across a wide range of sparse matrices from various scientific applications. Finally, we address a modern quantum physics problem to demonstrate the applicability of our method, achieving a speed-up of up to 4× on 832 cores of an Intel Sapphire Rapids cluster. Copyright © 2024, The Authors. All rights reserved.

关键词： Matrix algebra

A Short Tutorial on The Weisfeiler-Lehman Test And Its Variants

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A Short Tutorial on The Weisfeiler-Lehman Test And Its Varia...

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Ningyuan Teresa Huang Soledad Villar Applied Mathematics and Statistics Mathematical Institute for Data Science Johns Hopkins University

Graph neural networks are designed to learn functions on graphs. Typically, the relevant target functions are invariant with respect to actions by permutations. Therefore the design of some graph neural network architectures has been inspired by graph-isomorphism algorithms. The classical Weisfeiler-Lehman algorithm (WL)-a graph-isomorphism test based on color refinement-became relevant to the study of graph neural networks. The WL test can be generalized to a hierarchy of higher-order tests, known as k-WL. This hierarchy has been used to characterize the expressive power of graph neural networks, and to inspire the design of graph neural network architectures.A few variants of the WL hierarchy appear in the literature. The goal of this short note is pedagogical and practical: We explain the differences between the WL and folklore-WL formulations, with pointers to existing discussions in the literature. We illuminate the differences between the formulations by visualizing an example.

关键词： Visualization Conferences Signal processing algorithms Tutorials Color Tools Signal processing