We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.
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48 results for “mathematical coherence”
Site-specific recombination is an enzymatic process where two sites of precise sequence and orientation along a circle come together, are cleaved, and the ends are recombined. Site-specific recombination on a knotted substrate produces another knot or a two-component link depending on the relative orientation of the si…
Method guarantees coherent factuality for language model outputs in reasoning tasks.
problem Ensuring correctness of language model outputs in reasoning tasks.
method Developed a conformal-prediction-based method applied to subgraphs within a deducibility graph.
result Achieved coherent factuality across target coverage levels, 90% on stricter definition.
We study a space of coherent risk measures M_phi obtained as certain expansions of coherent elementary basis measures. In this space, the concept of ``Risk Aversion Function'' phi naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give nece…
A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a ``creation" connection with zero curvature over lagrangian submanifolds, is used to obtain a unified quantization including a noncommutative algebra of functions, its representa…
This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then e…
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analys…
New metric -coherence measures gradient alignment during training, revealing surprising memorization patterns.
problem Measuring and understanding the alignment of per-example gradients during training.
method Introducing -coherence as a metric to study gradient alignment, showing its advantages over existing metrics.
result Training with random labels leads to high -coherence, indicating common patterns even when generalization is not possible.
New coherence parameter for GNNs with Fourier measurements improves signal recovery.
problem Characterizing generative compressed sensing with Fourier measurements.
method Subspace counting arguments and high-dimensional probability theory.
result First known restricted isometry guarantee for generative compressed sensing with subsampled isometries.
Paper explores how to use mixed types of side information for better recommendations.
problem Challenges in using heterogeneous side information for recommender systems.
method Proposes a framework to jointly capture flat and hierarchical side information.
result Demonstrates significant performance gains over state-of-the-art methods.
Method transfers feature representation from large to small models using perception coherence.
problem Transfer feature representation from large to small models.
method Defines perception coherence, proposes loss function to minimize.
result Method outperforms or achieves on-par performance compared to strong baseline methods.
Go With the Flow, on Jupiter and Snow. Coherence From Model-Free Video Data without Trajectoriesphysics.data-an
Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image pro…
Pricing with coherent riskmath.PR
This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with negative risk; the other one defines a good deal as a trade with …
Expected Shortfall and Beyondcond-mat
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is d…
Inverse problems in imaging such as denoising, deblurring, superresolution (SR) have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their indisputable success, CNNs are not mathematically validated as to how and what …
Quantum algorithms for CVaR portfolio optimization face trade-offs between hardware coherence and expressibility.
problem Quantum algorithmic resilience for CVaR portfolio optimization
method WS-QAOA vs. HE-VQNN
result WS-QAOA provides exact theoretical mapping but suffers from hardware decoherence, while HE-VQNN preserves hardware coherence but lacks expressibility.
Concave Distortion Semigroupsq-fin.RM
The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a conca…
Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-foldshep-th
Let X be a Calabi-Yau 3-fold, T=D^b(coh(X)) the derived category of coherent sheaves on X, and Stab(T) the complex manifold of Bridgeland stability conditions Z on T. It is conjectured that one can define rational numbers J^a(Z) for Z in Stab(T) and a in the numerical Grothendieck group K(T) generalizing Donaldson-Thom…
New financial model revises risk measure under NA condition.
problem Revising classical financial mathematics with coherent risk measure on .
method Developed a new version of the fundamental theorem of asset pricing and provided dual representations.
result Set of risk-hedging prices is closed under NA condition.
Variance-Calibrated Modulation (VCM) addresses the likelihood trap in LLMs by reshaping the probability distribution before truncation.
problem LLMs fall into the likelihood trap, leading to repetitive degeneration and vocabulary dullness.
method VCM reshapes the probability distribution before truncation through Contextual Searchlight and Adaptive Self-Debiasing.
result VCM mitigates the likelihood trap across open-ended generation, factual QA, and mathematical reasoning.
In this work we study the Lebesgue property for convex risk measures on the space of bounded càdlàg random processes (). Lebesgue property has been defined for one period convex risk measures in \cite{Jo} and earlier had been studied in \cite{De} for coherent risk measures. We introduce and study th…
Two sets of high quality income data are analysed in detail, one set from the UK, one from the USA. It is firstly demonstrated that both a log-normal distribution and a Boltzmann distribution can give very accurate fits to both these data sets. The absence of a power tail in the US data set is then discussed. Taken in …
We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies or hydrodynamics, though using the same group theoretical methods and despite the well known couplings existing betwee…
This paper provides a PAC-Bayesian bound for CVaR in machine learning.
problem Learning algorithms minimizing CVaR of empirical loss.
method Generalization bound of PAC-Bayesian type, reducing CVaR estimation to expectation estimation.
result The bound is small when empirical CVaR is small, providing concentration inequalities for CVaR.
Unified theory of deep learning from approximation to emergence.
problem Understanding the mechanisms behind deep learning.
method Unified, proof-oriented approach tracing from classical foundations to contemporary mechanisms.
result Unified theory explaining deep learning from approximation to emergence.
The paper synthesizes the mathematics of modeling the future.
problem Modeling the future
method Unified mathematical synthesis
result Explicit connection of classical objects into a unified forecasting calculus
Equation Embeddingsstat.ML
We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good representations of equations by using the representations of their surrounding …
The paper derives Einstein tensors for a family of α-connections on quasi-statistical manifolds.
problem Deriving Einstein tensors for a new family of connections.
method Developed mathematical foundations of statistical and quasi-statistical manifolds, including dual and equiaffine connections.
result Explicit expressions for curvatures and Einstein tensors of the α-connections.
Coherent manifoldsmath-ph
Defines coherent manifolds and their quantum applications.
problem Understanding quantum spaces and coherent states.
method Generalizes quantum field theory and Schrödinger equation solutions.
result Solves Schrödinger equation on coherent manifolds.
CoRe method improves time series forecasting coherency without strict constraints.
problem Noisy hierarchical time series data that doesn't perfectly adhere to aggregation constraints.
method Coherency Regularization using neural networks.
result Improved forecast accuracy and coherence, especially in noisy data scenarios.
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …
Probabilistic aspects of financeq-fin.PR
In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability. In this survey paper, we review some of these developments and point to some ar…
We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition (DMD) on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this case financial market dynamics, in an equation-free manner by decomposing the s…
Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.
problem Identifying and visualizing coherence among multiple time series.
method Fast spectral similarity based on cosine similarity metrics of Fourier-transformed signals and sparse time-frequency wavelet coherence.
result Scalable real-time system for low-latency inference and monitoring of inter-signal relationships.
Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-foldsmath.DG
This paper concerns orientability of moduli spaces of Spin(7)-instantons on compact 8-manifolds with Spin(7)-structure for the Lie groups SU() and U(), and of moduli spaces of coherent sheaves on Calabi-Yau 4-folds. Such orientations are needed to define enumerative invariants 'counting' Spin(7) instantons, o…
Unified model improves coherence tasks, especially local contexts.
problem Existing neural coherence models struggle with local context tasks.
method Unified neural framework integrating grammar, relations, and patterns.
result Unified model outperforms existing models significantly.
Sequential portfolio selection has attracted increasing interests in the machine learning and quantitative finance communities in recent years. As a mathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision making under …
The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert space and a simple geometric interpretation of Calabi's diastasis follows.
Many predictive tasks, such as diagnosing a patient based on their medical chart, are ultimately defined by the decisions of human experts. Unfortunately, encoding experts' knowledge is often time consuming and expensive. We propose a simple way to use fuzzy and informal knowledge from experts to guide discovery of int…
A framework evaluates synthetic tabular data quality objectively.
problem Lack of an objective interpretation of tabular data metrics.
method Proposes a single mathematical objective for synthetic tabular data distribution, structurally decomposes it, and unifies existing metrics.
result Synthesizers that represent tabular structure outperform other methods, especially on smaller datasets.
An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, or…
Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for quantile-based coherent risk measures and related utility functionals. Typically, these solut…
Paper constructs Chern character for coherent sheaves.
problem Chern character for coherent sheaves with values in Bott-Chern cohomology.
method Based on Block's fundamental construction, constructs Chern character.
result Proves Riemann-Roch-Grothendieck formula for coherent sheaves.
-Bundlesmath.AT
This article reviews -bundles and their applications in geometry and physics.
problem Understanding higher bundles in geometry and physics.
method An -categorical formulation of higher bundles.
result Identification of higher bundles in various contexts.
The paper constructs minimal coherent filling pairs on surfaces.
problem Finding minimal intersecting coherent filling pairs on surfaces.
method Geometric procedure starting from a torus filling pair.
result Construction of minimal intersecting coherent filling pairs on for .
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training …
Paper defines dynamical coherence for flows and proves it under specific conditions.
problem Understanding the dynamics of partially hyperbolic flows.
method Introduces dynamical coherence and proves it for flows with a specific foliation.
result Dynamical coherence proved for flows with a particular foliation.
Develops equivariant Chern characters for coherent sheaves with group actions.
problem Computing Chern characters for coherent sheaves on manifolds with group actions.
method Introduces equivariant Chern characters and proves Riemann-Roch-Grothendieck theorem in Bott-Chern cohomology.
result Establishes a Riemann-Roch-Grothendieck theorem for coherent sheaves with finite group actions.