Computational mathematics | EPFL Graph Search

Computational mathematics is an area of mathematics devoted to the interaction between mathematics and computer computation. A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful. This involves in particular algorithm design, computational complexity, numerical methods and computer algebra. Computational mathematics refers also to the use of computers for mathematics itself. This includes mathematical experimentation for establishing conjectures (particularly in number theory), the use of computers for proving theorems (for example the four color theorem), and the design and use of proof assistants. Computational mathematics emerged as a distinct part of applied mathematics by the early 1950s. Currently, computational mathematics can refer to or include: Computational science, also known as scientific computation or computational engineering Solving mathematical problems by computer simulation as opposed to analytic methods of applied mathematics Numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations Stochastic methods, such as Monte Carlo methods and other representations of uncertainty in scientific computation The mathematics of scientific computation, in particular numerical analysis, the theory of numerical methods Computational complexity Computer algebra and computer algebra systems Computer-assisted research in various areas of mathematics, such as logic (automated theorem proving), discrete mathematics, combinatorics, number theory, and computational algebraic topology Cryptography and computer security, which involve, in particular, research on primality testing, factorization, elliptic curves, and mathematics of blockchain Computational linguistics, the use of mathematical and computer techniques in natural languages Computational algebraic geometry Computational group theory Computational geometry Computational number theory Computational topology Computational statistics Algorithmic information theory Algorithmic game theory Mathematical economics, the use of mathematics in economics, finance and, to certain extents, of accounting.

Technology Strategy in Dynamic Environments: A Computational Analysis of the Automation of Routines, the Organization of AI, and the Evaluation of Technology Risk

Maximilian Wieland Hofer

In this dissertation, I develop theory and evidence to argue that new technologies are central to how firms organize to create and capture value. I use computational methods such as reinforcement learning and probabilistic topic modeling to investigate three topics: the automation of routines, the organization of artificial intelligence (AI), and the evaluation of technology risk. Overall, I argue that new technologies are not a panacea for the firm but require deliberate strategic planning to manage the potential downsides of myopic automation, AI interdependencies, and the disclosure of technology risks.In the first essay, I argue that while automation can increase productivity by reducing the costs of coordinating individuals, the automation of routines can also incur an indirect opportunity cost due to slow adaptation to environmental change. I develop a reinforcement learning simulation to model the impact of automation on the returns from the division of labor in dynamic environments and to show how automation incurs opportunity costs through lost learning and slow adaptation. Moreover, automation can be suboptimal when it brings about myopic behavior, i.e. high returns from the division of labor in the short term, but negative returns in the long term. Given the simulation results, I argue that firms need dynamic routines to simultaneously balance learning and automation. I open-source the simulation platform as OrgSim-RL on GitHub.In the second essay, I argue that a data-driven culture - what I define as a Data Clan - can help to coordinate complex interdependencies between AI components within a firm. I analyze in-depth semi-structured interview data with a hierarchical stochastic block model (hSBM) and hand-coding to find that managers focus primarily on building a strong culture and establishing high-quality data assets when allocating resources to AI initiatives. Given the results, I inductively develop implications for theory and argue that the emergence of a Data Clan can be a governance mechanism to reduce coordination frictions and build a competitive advantage in the age of AI.In the third essay, I argue that investors require a higher initial return to take on more technology risk disclosure during an IPO. I quantify the magnitude of disclosed risk and the risk disclosure topics based on a latent Dirichlet allocation (LDA) topic model of IPO prospectus text and find a return-for-risk association between text-based technology risk disclosure and underpricing. The study also finds evidence that owning granted patents is associated with a lower return-for-risk association, suggesting that intellectual property allows the disclosure of risk without losing the competitive advantage. I open-source the code for quantifying risk disclosure as RiskyData-LDA on GitHub.In summary, this dissertation develops theory and finds evidence across three essays to argue that leveraging new technologies requires deliberate strategic planning to manage potential downsides of new technologies, such as the opportunity costs of automation, coordination costs, and costs associated with raising capital. The results suggest three mitigating solutions: dynamic routines to balance learning and automation, a Data Clan to improve coordination, and disclosure through patents to reduce underpricing.

EPFL2022

Prenatal auditory experience and its sequelae

Lukas Vogelsang, Marin Vogelsang

Towards the end of the second trimester of gestation, a human fetus is able to register environmental sounds. This in utero auditory experience is characterized by comprising strongly low-pass-filtered versions of sounds from the external world. Here, we present computational tests of the hypothesis that this early exposure to severely degraded auditory inputs serves an adaptive purpose-it may induce the neural development of extended temporal integration. Such integration can facilitate the detection of information carried by low-frequency variations in the auditory signal, including emotional or other prosodic content. To test this prediction, we characterized the impact of several training regimens, biomimetic and otherwise, on a computational model system trained and tested on the task of emotion recognition. We find that training with an auditory trajectory recapitulating that of a neurotypical infant in the pre-to-postnatal period results in temporally extended receptive field structures and yields the best subsequent accuracy and generalization performance on the task of emotion recognition. This strongly suggests that the progression from low-pass-filtered to full-frequency inputs is likely to be an adaptive feature of our development, conferring significant benefits to later auditory processing abilities relying on temporally extended analyses. Additionally, this finding can help explain some of the auditory impairments associated with preterm births, suggests guidelines for the design of auditory environments in neonatal care units, and points to enhanced training procedures for computational models.

WILEY2022

Simulation of volume changes of cement paste at early age

Karen Scrivener, Amor Guidoum, Ines Jaouadi

The evolution of early age mechanical properties and volume change of cement paste is performed through Finite Element analysis on a 3D computer-generated cement paste. The time evolution of the hydrating microstructure is generated by μic(mike), a vectorial hydration model which takes into account the Particle Size Distribution (PSD) of anhydrous cement particles, the w/c ratio, the filler content and different hydration kinetics mechanisms such as nucleation, growth and diffusion. The microstructure geometry is then discretized into a finite element mesh. At each hydration step, the capillary depression is computed according to Laplace-Kelvin equation and applied on the pore space generated by the hydration model. Then, the autogenous shrinkage corresponds to the overall load-free deformation of the computational volume. Two constitutive models are used. The first one is a purely elastic model where macroscopic stress depends on the total porosity only. The second one is a poroelastic model which takes into account the fluid-solid interaction and the de-saturation effect. In parallel to the modeling work, a systematic experimental study has been performed on series of white cement pastes prepared different finenesses and various water-cement ratios. Many characterization techniques were used in the experimental study: chemical shrinkage, evolution of relative humidity, mercury intrusion porosimetry (MIP), x-ray diffraction (XRD), linear and volumetric autogenous shrinkage and ultrasonic wave propagation measurements. The numerical results are compared with experiment data and it is shown that the poroelastic model provides the best agreement to the experimental results. The remaining gap between the modeling and the experiment is discussed and future developments are outlined.

2009

Technology Strategy in Dynamic Environments: A Computational Analysis of the Automation of Routines, the Organization of AI, and the Evaluation of Technology Risk

Maximilian Wieland Hofer

EPFL2022