Generative adversarial networks improve pseudo-random number generation.
problem Improving the quality of pseudo-random number generators.
method Training a GAN to generate sequences that are hard for an adversary to predict.
result GAN-trained neural networks can produce pseudo-random sequences with good statistical properties.
Transformers can predict pseudo-random sequences from LCGs with unseen parameters and moduli.
problem Learning pseudo-random number sequences from linear congruential generators with unknown parameters and moduli.
method Investigated the ability of Transformers to learn LCG sequences with varying complexity and moduli. Analyzed embedding layers and attention patterns.
result Transformers can predict pseudo-random sequences from LCGs with unseen parameters and moduli, up to mexttest=216, using a two-step strategy. Quantum algorithm reduces qubit usage for Monte Carlo simulations.
problem High qubit requirements for Monte Carlo simulations on quantum computers.
method Use of pseudo-random number generator (PRNG) on a quantum circuit.
result Significant reduction in qubit usage without sacrificing quantum speed.
Measurements of cosmic microwave background (CMB) anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. Using the direct bou…
Study finds no significant difference in neural network weights with quantum random numbers.
problem Effects of biased quantum random numbers on neural network initialization.
method Empirical study using quantum hardware and classical pseudo-random numbers.
result No statistically significant difference found between quantum random numbers and other types.
Study reveals finite-size effects and sensitivity to random numbers in Levy-Levy-Solomon model.
problem Finite-size effects and sensitivity to random numbers in Levy-Levy-Solomon model.
method Simulations and analysis of Levy-Levy-Solomon model with different random number generators and stopping criteria.
result Low-quality pseudo random number generators significantly impact simulation results.
Paper presents quantum algorithms for pricing financial derivatives using complex models.
problem Implementing complex financial models like local volatility on quantum computers.
method Developed two quantum circuit implementations for local volatility model.
result Demonstrated reduced qubit requirements for local volatility model.
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
New adversarial examples from crypto generators show robust machine learning challenges.
problem Adversarial examples in machine learning due to cryptographic pseudo-random generators.
method Constructing a binary classification task with maximal robustness and proving computational hardness under cryptographic assumptions.
result Maximally robust classifiers can tolerate perturbations of size comparable to the examples themselves, highlighting computational hardness.
We formulate statistical watermarking as hypothesis testing and establish near-optimal bounds.
problem Statistical watermarking in the context of hypothesis testing.
method Formulated as a hypothesis testing problem, using coupling of output tokens and rejection regions.
result Established nearly matching upper and lower bounds on the number of i.i.d. tokens required for small Type I and Type II errors.
New cross-validation method reduces bias and improves prediction error.
problem Subsampling bias in k-fold cross-validation.
method Best-discrepancy systematic sampling.
result Reduces subsampling bias and improves prediction error.
Study tests financial market efficiency using random number generator tests.
problem Check for informational efficiencies in financial markets.
method Analysed binary daily returns as random number generators, split analysis by annual and company levels, investigated longer-term efficiency over Nasdaq-listed companies.
result Information efficiency varies across years and reflects large-scale market impacts.
Quantum computers outperform classical methods in density modeling.
problem Density modeling with quantum computers.
method Quantum-classical separation for density modeling.
result Quantum computers offer a super-polynomial advantage over classical algorithms for density modeling.
Bayesian Neural Networks (BNNs) have been proposed to address the problem of model uncertainty in training and inference. By introducing weights associated with conditioned probability distributions, BNNs are capable of resolving the overfitting issue commonly seen in conventional neural networks and allow for small-da…
Energy-efficient sampling for machine learning using magnetic tunnel junctions.
problem Costly and inefficient random sampling in machine learning.
method Energy-efficient algorithm using stochastic magnetic tunnel junctions for uniform Float16 sampling.
result Higher energy efficiency than state-of-the-art algorithms, with a minimum factor of 9721.
AGMMNs improve learning of copula models by adaptively selecting kernels.
problem Learning dependence structures in copula models.
method Adaptive bandwidth selection for MMD in GMMNs, increasing kernels based on validation loss.
result AGMMNs significantly improve training performance over GMMNs and parametric models.
The paper develops methods to analyze sensitivity in stochastic models using surrogate models.
problem Quantifying the impact of input variability on stochastic simulators with randomness.
method The authors propose using generalized lambda models to emulate response distributions of stochastic simulators and estimate sensitivity indices.
result The proposed method can estimate sensitivity indices even with strong heteroskedasticity and small signal-to-noise ratio.
Generative neural networks enable quasi-random sampling for diverse multivariate distributions.
problem Generating quasi-random samples for complex multivariate distributions is challenging and restricted.
method Generative moment matching networks (GMMNs) for quasi-random sampling.
result GMMNs allow quasi-random sampling for a broader range of multivariate distributions.
A method extracts binary features directly from CS measurements for compressive image classification.
problem Efficiently classify images using compressive sensing without reconstruction.
method DCT-based approach for binary feature extraction from CS measurements, feature fusion with CNN features.
result Fused features outperform state-of-the-art methods in image classification.
Improved neural network training in low-dimensional random bases.
problem Inefficient optimization in large-scale neural networks.
method Re-draw random subspace at each training step, apply independent projections to different network parts.
result Significantly better optimization performance and efficiency.
Unified framework for online LLM watermark detection using e-processes.
problem Detecting AI-generated text from human-written content in online settings.
method Unified framework based on e-processes for anytime-valid hypothesis testing on independence.
result Proposed methods achieve competitive performance in watermark detection.
This study examines how financial tick data becomes more random with time aggregation.
problem Investigating the randomness of financial tick data over time.
method Applied statistical randomness tests from NIST and TestU01 batteries to ultra-high frequency financial data.
result Financial tick data becomes increasingly random as the aggregation level of transaction time increases.
We improve likelihood-free inference using distillation of importance sampling.
problem Challenging likelihood-free inference with high-dimensional, dependent posterior.
method Approximate posterior with normalizing flows trained on likelihood-free importance sampling.
result Improved accuracy in inference without needing summary statistics.
New lower bounds show learning intersections of halfspaces is hard even for a few halfspaces.
problem Learning intersections of halfspaces in polynomial time under standard assumptions.
method Unified connection to parallel pancakes distribution for proving hardness.
result Learning ω(loglogN) halfspaces in dimension N requires super-polynomial time under standard assumptions. New DGA detection models use side info to improve robustness.
problem Adversaries craft domain names to evade DGA detection.
method Train deep learning and RF classifiers using domain name and side info.
result Models using both domain name and side info are more robust.
Echo state network (ESN) is viewed as a temporal non-orthogonal expansion with pseudo-random parameters. Such expansions naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the variance of the tea…
Paper characterizes relation numbers for parabolic two-generator groups.
problem Determining relation numbers for parabolic two-generator groups.
method Characterized relation numbers by equivalence to roots of generalized Chebyshev polynomials.
result Deciding relation numbers can be done by checking finitely many polynomials.
Paper refines generating function for 2-bridge knot groups.
problem Determining the number of epimorphisms between 2-bridge knot groups.
method Refined generating function considering genus and crossing number.
result Improved formula for epimorphisms between 2-bridge knot groups.
Jablan and Radović originally defined two invariants called the Meander number and OGC number of knots for certain classes of knots. We generalize these definitions to all knots and name the straight number and contained straight number of a knot, respectively, and prove they are well defined. We answer two questions a…
Torsion and Betti numbers for knots are special cases of more general invariants associated to a finitely generated group G and epimorphism from G to the integers. The sequence of Betti numbers is always periodic; under mild hypotheses, the sequence of torsion numbers satisfies a linear homogeneous recurrence relation …
Ascending numbers are determined for 64 knots with at most n=10 crossings. After proving the theorem about the signature of alternating knot families, we distinguished all families of knots obtained from generating alternating knots with at most 10 crossings, for which the unknotting number can be confirmed by using th…
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numb…
The study bounds growth of Hodge numbers and computes L2-Betti numbers for irregular varieties.
problem Bounding growth of normalized Hodge numbers and computing L2-Betti numbers for irregular varieties. method Analysis of abelian covers, weak generic Nakano vanishing theorem, and convergence of plurigenera.
result Optimal bounds on the growth of normalized Hodge numbers and computation of L2-Betti numbers. The paper introduces generalized Lelong numbers for currents and their applications in intersection theory.
problem Defining and studying generalized Lelong numbers for currents in intersection theory.
method Formulating generalized Lelong numbers for closed smooth (j,j)-forms, defining horizontal dimension, and establishing properties and formulas.
result Effective sufficient conditions for defining and continuity of intersections of positive closed currents.
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
problem Analyzing crossing and rotation numbers of cycles in plane immersions of graphs.
method Generic immersions and Legendrian embeddings of graphs, focusing on cycles of specific lengths.
result Sum of rotation numbers of all 5-cycles is even, and sum of crossing numbers is odd.
Study Hodge-de Rham numbers for almost complex 4-manifolds, extending properties from complex surfaces.
problem Understanding Hodge-de Rham numbers for almost complex 4-manifolds.
method Introduced and studied Hodge-de Rham numbers, extending properties from complex surfaces.
result All Hodge-de Rham numbers for compact almost complex 4-manifolds are determined by the cohomology, except for one (the irregularity).
Study of generalized knots and links, proving inequality involving crossing number and braid index.
problem Proving an inequality involving the minimal crossing number and braid index for generalized knots and links.
method Introducing generalized crossings and moves, proving inequality for generalized knots and links.
result Proved inequality involving total crossing number and braid index for generalized knots and links.
Non-Euclidean number rings have non-integral Steinberg modules.
problem Characterizing when Steinberg modules are generated by integral elements.
method Analyzing special linear groups over non-Euclidean imaginary number rings.
result Steinberg modules are not generated by integral elements in non-Euclidean rings.
We give a tropical interpretation of Hurwitz numbers extending the one discovered in \cite{CJM}. In addition we treat a generalization of Hurwitz numbers for surfaces with boundary which we call open Hurwitz numbers.
Study of Fishburn numbers and their congruences for torus knots.
problem Arithmetic properties of Fishburn numbers and congruences for torus knots.
method Use of divisibility results and a new identity for Kontsevich-Zagier series.
result Prove prime power congruences for generalized Fishburn numbers.
Defines linking number and Milnor invariants, their properties.
problem None explicitly stated; definitions and properties are discussed.
method Definitions and properties of linking number and Milnor invariants are discussed.
result Definitions and properties of linking number and Milnor invariants are established.
The paper generalizes Segre and Verlinde numbers for surfaces with holomorphic 2-forms.
problem Generalizing Segre and Verlinde numbers for surfaces with holomorphic 2-forms.
method Using Mochizuki's formula and Seiberg-Witten invariants, derive universal functions and prove topological invariants.
result Certain canonical virtual Segre and Verlinde numbers of general type surfaces are topological invariants.
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
We analyze how a family of essential annuli in a compact 3-manifold will induce, from a strongly irreducible generalized Heegaard splitting of the ambient manifold, generalized Heegaard splittings of the complementary components. There are specific applications to the subadditivity of tunnel number of knots, improving …
Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
problem Understanding the relationship between unknotting numbers and crossing numbers of spatial embeddings of planar graphs.
method Analyzing specific examples of planar graphs and their spatial embeddings to find counterexamples.
result There exist planar graphs and their spatial embeddings where the unknotting number is greater than half the crossing number.
In this paper, we denone the generalized bicomplex numbers and give some algebraic properties of them. Also, we show that some hyperquadrics in R4 and R42 are Lie groups by using generalized bicomplex number product and obtain Lie algebras of these Lie groups. Morever, by using tensor product surfaces, we determine som…
New bounds on knot complexity defined via band number and surface diagrams.
problem Understanding the complexity of knots and their generalizations.
method Defining and analyzing band number, using broken surface diagrams and 3-manifold embeddings.
result Band number is an upper bound on double slice genus, a knot complexity measure.
Method generates random numbers from sensor noise, improving accuracy and speed.
problem Improving accuracy and speed of Monte Carlo integration.
method Sampling a physical process in a controlled environment.
result Reduces error of Monte Carlo integration by 10^68 times while doubling speed.