Modeling language as a matrix product state with probability measures.
problem Understanding the structure of natural language.
method Statistical model using complex matrices and matrix product states.
result Language can be represented as a translation invariant matrix product state.
A new method creates simpler, more interpretable decision trees from complex ensembles.
problem Complex tree ensembles reduce interpretability and control over machine learning models.
method Dynamic-programming based algorithm for finding a minimum-size decision tree.
result Optimal born-again trees are simpler and more interpretable than original ensembles.
New definition of Born geometry connects to known geometries.
problem Defining and understanding Born geometries.
method Using Künneth structures and recursion operators.
result Born connection derived from Künneth connection for integrable geometries.
The Björling problem is explored for Born-Infeld solitons.
problem Solving the Björling problem for Born-Infeld solitons.
method Analyzes locally Born-Infeld soliton surfaces and graph-like surfaces, presenting representation formulae.
result Results about representation formulae for Born-Infeld solitons.
Born Lie algebras classified up to 6D, with integrable metrics studied.
problem Classifying and understanding Born Lie algebras.
method Bicross product construction from pseudo-Riemannian Lie algebras.
result Classification of Lie algebras up to 6D with integrable Born structures.
Neural networks learn higher-order derivatives for physics problems.
problem Lack of higher-order derivatives in neural networks for theoretical physics.
method Graph-theoretical approach to assign diagrams to partial derivatives, iterative NN perturbation theory.
result NNs can learn higher-order derivatives, improving machine-learned approximations.
Study equivalence between Hessian and Born structures on tangent bundles.
problem Equivalence between Hessian and Born structures on tangent bundles.
method Analyzing conditions for Hessian structures and integrability of induced almost Born structures.
result Conditions for equivalence between Hessian and Born structures are established.
Born-Infeld solitons linked to maximal surfaces via Ramanujan's identities.
problem Understanding Born-Infeld solitons and their relation to maximal surfaces.
method Combining Born-Infeld solitons with maximal surfaces, using Ramanujan's identities.
result Derived new identities from Weierstrass-Enneper representation of maximal surfaces.
Study Born-Infeld solitons and solve Björling problem for them.
problem Existence and non-uniqueness of solutions to the Björling problem for Born-Infeld solitons.
method Two approaches: treating as time-like minimal surfaces or using Barbashov-Chernikov representation.
result Solution to Björling problem may not be unique.
Proves a unique connection for Born geometry.
problem Consistency of string dynamics under T-duality.
method Proves a unique connection preserving the Born structure.
result Resolves a fundamental ambiguity in double field theory.
New MBL hidden Born machine learns various tasks.
problem Learning from quantum many-body systems.
method MBL dynamics and hidden units for training.
result Enhanced trainability and stability in learning.
Summary of para-Hermitian geometry for T-duality in string theory.
problem Describing T-duality in string theory with a covariant approach.
method Introducing para-Hermitian geometry and Born geometry to enhance the kinematical setup.
result A generalized differentiable structure on the doubled space allows for the recovery of physical spacetime.
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
We define a new geometric framework for string theory.
problem String theory and its symmetries.
method Para-Hermitian geometry and Born geometry.
result A geometric interpretation of string theory symmetries.
A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.
problem Optimization challenges in non-convex loss functions and machine learning tasks.
method Discretization of Born-Infeld dynamics for energy-conserving Hamiltonian optimization.
result The method avoids high local minima and outperforms traditional methods in shallow valleys.
Study on a new Yang-Mills type functional and its critical points.
problem Deriving a new functional from Yang-Mills and Born-Infeld theories.
method First and second variation formulas established.
result Existence of critical points proved.
The Monster tower, also known as the Semple tower, is a sequence of manifolds with distributions of interest to both differential and algebraic geometers. Each manifold is a projective bundle over the previous. Moreover, each level is a fiber compactified jet bundle equipped with an action of finite jets of the diffeom…
We obtain the Weierstrass-Enneper representation for maximal graphs(whose Gauss map is one-one) in Lorentz-Minkowski space. For this we use the method of Barbishov and Chernikov, which they have used to find the solutions of Born-Infeld equation in hodographic coordinates. We could use their method in our case, because…
The paper explores connections between three equations via Wick rotations and symmetries.
problem Investigating relations between solutions to specific equations under Wick rotations.
method Analyzing symmetries and transformations of solutions to the minimal surface, zero mean curvature, and Born-Infeld equations.
result Existence conditions and transformations of real and imaginary solutions under Wick rotations.
The paper studies graphs with prescribed Lorentzian mean curvature and their relation to Born-Infeld theory.
problem Existence and regularity of spacelike graphs with prescribed Lorentzian mean curvature.
method Analyzes the action functional and uses variational methods to study the existence and regularity of the graph function.
result Sufficient conditions are found to ensure that the graph function solves the Born-Infeld equation and enjoys improved regularity estimates.
Adversarial quantum-classical model learns and infers data faster.
problem Training quantum circuits is harder than classical neural networks.
method Coupling quantum generator with classical discriminator for training.
result Quantum circuit can infer missing data with quadratic speed up.
In this paper a convergent series expansion is constructed to solve the prescribed mean curvature equation for n-dimensional hypersurfaces in n+1 dimensional Euclidean or Minkowskian space(time) which are graphs of a smooth real function u, and whose mean curvature function H is not too large in Hoelder norm, and integ…
Quantum circuits can generate samples but lack likelihood; we devise a gradient-based learning algorithm.
problem Quantum circuits lack likelihood for generating samples, making training difficult.
method Developed a gradient-based learning algorithm to minimize the kernelized maximum mean discrepancy loss.
result Demonstrated the effectiveness of the algorithm on generative modeling tasks.
Quantum machine learning improves pulsar classification in radio astronomy.
problem Improving classification of pulsars in radio astronomy.
method Used a Born machine (quantum neural network) with a single-qubit architecture.
result Comparable accuracies to classical machine learning methods achieved.
Explains the Schwarz lemma in lecture notes.
problem None explicitly stated; focuses on explanation.
method Expository notes on the Schwarz lemma.
result Explains the Schwarz lemma.
The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.
problem Decomposing the height function of different types of surfaces into simpler components.
method Using Euler-Ramanujan identities and Weierstrass-Enneper representation to decompose height functions of minimal, maximal, timelike minimal, and Born-Infeld surfaces.
result The height function of various surfaces can be expressed as a finite sum of scaled and translated versions of itself.
The study compares classical and quantum information-based unsupervised generative models.
problem Comparing classical and quantum information-based unsupervised generative models.
method Analyzing information theoretical bounds and comparing RBM architectures on MNIST datasets.
result Quantum information-based models outperform classical models in certain scenarios.
We prove long time existence and convergence results for the pluriclosed flow, which imply geometric and topological classification theorems for generalized Kähler structures. Our approach centers on the reduction of pluriclosed flow to a degenerate parabolic equation for a (1,0)-form, introduced in \cite{ST2}. We ob…
Let F:[0,∞)→[0,∞) be a strictly increasing C2 function with F(0)=0. We unify the concepts of F-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce F-Yang-Mills fields, F-degree, F-lower degree, and generalized Yang-Mills-Born-Infeld…
Existence of minimizers and singular solutions for Hodge energy on manifolds.
problem Existence of minimizers and singular solutions for Hodge energy.
method Analyzing the generalized minimal surface energy on compact Riemannian manifolds.
result Existence of unique minimizers for k=1 and singular solutions for k>1. A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and Born-Infeld systems.
We present an overview of some older papers on involutory quandles, mostly from the times before the term "quandle" was born. It is meant as a reference guide, not (yet) as an expository article explaining what the involutory quandles are and what they are good for.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Ha…
Clarifies conditions for non-Abelian Dirac-Born-Infeld action's masslessness and dynamics.
problem Resolving a pull-push issue in constructing the non-Abelian Dirac-Born-Infeld action.
method Examines two admissible conditions (1) and (2) on differentiable maps in detail.
result Condition (1) alone implies masslessness of the connection, while (2) decouples the fuzzy cloud.
Shared classical randomness improves quantum generative models' output distributions.
problem Improving generative performance of shallow unitary quantum models.
method Introducing stochasticity into unitary quantum models via shared classical randomness.
result Shared classical randomness allows shallow unitary quantum models to represent a strictly larger family of distributions.
This is the written version of a talk given on 1 July 2009 at the XXV Max Born Symposium: the Planck Scale, held in Wroclaw, Poland. I review the possible transverse geometries to supersymmetric M2-brane configurations and discuss the representation-theoretic description of their conjectured dual superconformal Chern-S…
BANs outperform teachers in computer vision and language modeling.
problem Improving model performance while reducing model size.
method Train students identically to their teachers using KD.
result BANs achieve state-of-the-art performance on CIFAR-10 and CIFAR-100 datasets.
We show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize the case when the bound is reached.
Quantum circuit models learn better with specific initialization strategies.
problem Understanding and improving the optimization landscape of IQP-based generative models.
method Proved barren plateaus for random initialization, established lower bounds, and developed data-dependent initialization.
result Data-dependent initialization leads to faster convergence and better minimums.
We construct an expanding gradient Ricci soliton in dimension three over the topological manifold R x T^2 (the product of a line and a torus) that aproaches asymptotically a constant curvature cusp at one end, and a flat manifold on the other end. We prove that this is the only gradient soliton with this topology, prov…
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theor…
Survey para-Hermitian geometry and its applications in physics.
problem Capturing double field theory concepts on para-Hermitian manifolds.
method Geometric theory of Lagrangian and Hamiltonian systems, deformations of para-Kahler structures, non-linear connections, and weak integrability.
result Reproduce generalized fluxes in para-Hermitian geometry and describe their emergence.
Paper computes Alexander polynomials for arborescent links.
problem Explicit formulas for Alexander polynomials are hard to compute for most link families.
method Efficient method for arborescent links, using recursive polynomials.
result Explicit closed formulas for pretzel links derived.
In this article we consider the motion of relativistic strings in the Minkowski space R1+n. Those surfaces are known as a timelike minimal surface, and described by a system with n nonlinear wave equations of Born-Infeld type. By constructing a suitable Nash-Moser iteration scheme, we prove that the n…
We consider extensive data on Spanish international trades and population composition and, through statistical-mechanics and graph-theory driven analysis, we unveil that the social network made of native and foreign-born individuals plays a role in the evolution and in the diversification of trades. Indeed, migrants na…
New PG samplers improve inference in coupled state-space models.
problem Bayesian inference from multiple time series with shared parameters.
method Marginalized Particle Gibbs samplers for coupled state-space models.
result Improved parameter inference through shared information.
In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, by using a system of hodographic coordinates. This is done by using the method of solving the Born-Infeld equations by Whitham. We directly compute conformal coordinates on the minimal surf…
In this paper, we discuss a one parameter family of complex Born-Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B-I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples. We …