Book reviews Riemann's work's impact on math, philosophy, physics.
problem None explicitly stated, focuses on Riemann's contributions.
method Review of Riemann's work and its impact.
result Riemann's work has broad impacts on math, philosophy, physics.
Einstein's philosophy uses differential identities to derive GR field equations.
problem Constructing field theories in alternative geometries.
method Explains differential identities and their role in GR and PAP-geometry.
result Derived a more general differential identity in PAP-geometry.
Epicurus' philosophy aligns with Reinforcement Learning principles.
problem Misconceptions about Epicurean philosophy and its relation to RL.
method Analysis of Epicurus' letters and comparison with RL concepts.
result Epicurean hedonism objective function is equivalent to RL objective function.
Riemann's math ideas often come from physics, blending philosophy and science.
problem Separating Riemann's mathematical ideas from their physical origins.
method Overview of Riemann's work, emphasizing physical motivation and philosophical context.
result Riemann's mathematical results are deeply intertwined with physical reasoning and philosophical ideas.
Machine learning's data-centric philosophy conflicts with natural sciences' standards.
problem Conflict between machine learning's ontology and epistemology and natural sciences' practices.
method Identifying and analyzing contexts where ML can be beneficial or harmful in natural sciences.
result ML can enhance trustworthiness in causal inference but introduces biases in emulation and labeling.
Paper connects fair machine learning to political philosophy, highlighting flaws in ideal approaches.
problem Lack of natural formulation for social desiderata in machine learning.
method Proposes metrics and algorithms to satisfy subsets of fairness parities, trading off against utility.
result Misguided fair machine learning algorithms reflect broader flaws in ideal methodological approaches.
This book presents a methodology and philosophy of empirical science based on large scale lossless data compression. In this view a theory is scientific if it can be used to build a data compression program, and it is valuable if it can compress a standard benchmark database to a small size, taking into account the len…
Eliashberg simplifies singularities in geometry.
problem Complex singularities in geometric structures.
method Philosophy of the h-principle and simplification techniques.
result Simplified understanding of singularities in geometry.
Model credit ratings using economic states with Markov chains.
problem Credit rating migration influenced by economic state changes.
method Developed a Markov chain model for credit ratings conditional on economic states.
result Derived asymptotic behavior of the rating process using Markov theory.
Paper proposes a new AI design philosophy for distributed learning.
problem Designing AI systems that mimic human cognitive capabilities.
method Democratized learning (Dem-AI) with self-organized hierarchical agents.
result Self-organized learning systems can perform complex tasks more efficiently.
A new clustering algorithm inspired by Wittgenstein's philosophy.
problem Clustering data without assuming predefined cluster shapes or sizes.
method Wittgenstein's family resemblance concept applied to machine learning.
result WFR clustering algorithm effectively identifies clusters in data.
Formulates approach for guiding explanation types based on user specifications.
problem Creating explainable AI components from user-defined specifications.
method Develops a method for generating explanations based on user-defined specifications.
result Demonstrates feasibility of user-defined explanations for complex models like Bayesian networks and graph neural networks.
In the present work, torsion energy is defined. Its law of conservation is given. It is shown that this type of energy gives rise to a repulsive force which can be used to interpret supernovae type Ia observations, and consequently the accelerating expansion of the Universe. This interpretation is a pure geometric one …
Paper resolves apparent conflict between group and individual fairness.
problem Apparent conflict between group and individual fairness in machine learning.
method Theoretical discussions from fair machine learning, political, and legal philosophy.
result Individual and group fairness are not fundamentally in conflict.
This paper explores historical and philosophical aspects of angles and solid angles, inspired by Euler's work.
problem Understanding the historical context and philosophical implications of angles and solid angles.
method Historical review and analysis of mathematical and philosophical works.
result Questions raised by Euler about angles and solid angles are timeless and relevant to modern mathematics.
Pylearn2 is a machine learning research library. This does not just mean that it is a collection of machine learning algorithms that share a common API; it means that it has been designed for flexibility and extensibility in order to facilitate research projects that involve new or unusual use cases. In this paper we g…
Refines a key lemma in symplectic topology, improving its applicability.
problem Improving the applicability of the holonomic approximation lemma in symplectic topology.
method Careful quantitative geometry and Gromov's convex integration method.
result Establishes several refinements of the holonomic approximation lemma.
No free lunch theorems show all algorithms perform equally under uniform distribution.
problem Analyzing scenarios involving non-uniform distributions and comparing algorithms.
method No Free Lunch theorems applied to analyze and compare algorithms without distribution assumptions.
result Anti-cross-validation performs as well as cross-validation under non-uniform distributions.
This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace progress and thinking about the SYZ conjecture since its introduction in 1996. …
A new framework solves the causal frame problem using potential levels.
problem How to make decisions based on relevant information without considering irrelevant details.
method Introducing Potential Level (PL) and proposing a PL-based Inference Framework (PLIF).
result PLIF is consistent with causal judgment findings and makes testable predictions.
New boundary functions yield infinitely many solutions for minimal surfaces.
problem Existence of multiple solutions for minimal surfaces.
method Lawson-Osserman constructions and Dirichlet problem analysis.
result Infinitely many analytic solutions and at least one nonsmooth solution.
Graphs help study singular points of algebraic surfaces.
problem Understanding singular points of algebraic surfaces.
method Introduced special kinds of graphs and developed a calculus with graphs.
result Graphs provide a new way to classify and study singular points.
This paper aims at transferring the philosophy behind Heath-Jarrow-Morton to the modelling of call options with all strikes and maturities. Contrary to the approach by Carmona and Nadtochiy (2009) and related to the recent contribution Carmona and Nadtochiy (2012) by the same authors, the key parametrisation of our app…
Interdisciplinary fields like econophysics and sociophysics can enrich their parent disciplines.
problem Whether interdisciplinary fields can contribute to their parent disciplines.
method Literature review on history and philosophy of science.
result Interdisciplinary fields have a long history and are likely to continue contributing to their parent disciplines.
New algorithms learn in complex decision-making problems with smooth transitions.
problem Learning in complex decision-making problems with smooth transitions.
method UCB and PSRL philosophies applied to episodic Markov decision processes with kernel approximation.
result Low regret learning achieved in continuous state and action spaces.
Machine learning disciplines shift values, not just model types.
problem Values influence machine learning discipline and model types.
method Philosophy of science lens, conceptual framework analysis.
result Disciplinary shifts encode social and political values.
This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically invariant character of curvature, struggled with elimination computations in order…
Distiller simplifies DNN compression research with a Python package.
problem Efficiently compressing deep neural networks.
method Open-source Python package with DNN compression algorithms.
result Facilitates new research and learning tasks in DNN compression.
Floer theory uses categories to construct 3-manifold invariants.
problem Constructing 3-manifold invariants via decomposition and functors.
method Floer field theory via decomposition in bordism category and functor to symplectic category.
result Floer theory has potential 4-dimensional extensions.
Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is cartesian closed. By emancipating microlinearity from within a well-adapted model …
The study examines how knots relate based on a specific map property.
problem Understanding the complexity of knots through a map property.
method Examines knots through a degree 1 map property between their exteriors.
result Supports the idea that more complex knots have a higher map property.
LAGE is a systematic framework developed in Java. The motivation of LAGE is to provide a scalable and parallel solution to reconstruct Gene Regulatory Networks (GRNs) from continuous gene expression data for very large amount of genes. The basic idea of our framework is motivated by the philosophy of divideand-conquer.…
This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing the mathematical Fundamental Theory of Asset Pricing with reference to the emergen…
New approach for large-scale distributed learning systems that improve generalization performance.
problem Transitioning from centralized to distributed AI systems for complex learning tasks.
method Self-organizing hierarchical structuring mechanism based on agglomerative clustering, hierarchical generalization, and personalized learning.
result Demonstrates better generalization performance compared to conventional federated learning algorithms.
The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have emancipated microlinearity from within well-adapted models…
New proof of trapped surface formation using signature for decay rates.
problem Trapped surface formation in gravitational collapse.
method Systematic approach with signature for decay rates, rescaling argument.
result Reproof and extension of a scale-critical theorem.
Bayesian framework explains diverse explanatory values.
problem Understanding and predicting human preferences for explanations.
method Developed a Bayesian account to integrate various explanatory values.
result Core values from psychology, statistics, and philosophy emerge from a common framework.
In [Topology 35 (1996) 1005--1023] J H Rubinstein and M Scharlemann, using Cerf Theory, developed tools for comparing Heegaard splittings of irreducible, non-Haken manifolds. As a corollary of their work they obtained a new proof of Waldhausen's uniqueness of Heegaard splittings of S^3. In this note we use Cerf Theory …
We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions of canonical toric singularities (already found by Goldstein), proper versions of these fibrations, and fibrations on flat deformations of c…
The study characterizes lamination limits and homeomorphisms in 3D handlebodies.
problem Characterizing lamination limits and homeomorphisms in 3D handlebodies.
method Using Hausdorff limits and commensurability of laminations, the study characterizes lamination limits and homeomorphisms.
result A characterization of when a non-minimal lamination is a Hausdorff limit of meridians and related characterization of homeomorphisms.
Develops a framework for modeling interest rate markets with jumps.
problem Stochastic discontinuities in interest rate markets.
method Extended HJM framework with stochastic discontinuities, affine semimartingales.
result Fundamental theorem of asset pricing based on NAFLVR.
Spaces over BO are equivalent to thickened manifolds.
problem Understanding embeddings of manifolds in higher dimensions.
method Formal identification of manifolds with their thickened versions, using geometric constructions.
result The infinity-category of thickened smooth manifolds is equivalent to the infinity-category of finite spaces over BO.
ATHENA builds flexible defenses against adversarial attacks.
problem Extensive research on adversarial attacks is domain-specific and cannot be easily extended.
method Designing an extensible framework based on diverse weak defenses.
result Comprehensive empirical study demonstrates the effectiveness of ATHENA.
In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian pa…
This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent coadjoint orbit in the philosophy of Kirillov-Kostant. We begin by applying methods fro…
The JLS model explains market crashes as critical phenomena.
problem Understanding market crashes as critical points.
method Study of Johansen-Ledoit-Sornette model.
result The JLS model provides a causal explanation of market crashes.
W-entropy and reduced volume for the Ricci flow were introduced by Perelman, which had proved their importance in the study of the Ricci flow. L. Ni studied the analogous concepts for the linear heat equation on the static manifolds, and established an equation which links the large time behavior of these t…
Edge computing tackles dynamic data in IIoT with incremental learning.
problem Latency and bandwidth limitations in IoT devices.
method Incremental learning applied to edge-computing systems for continual learning.
result Reduces catastrophic forgetting and provides efficient real-time quality control.