Study groups of order 64 and non-homeomorphic double Kodaira fibrations with same invariants.
problem Investigate finite quotients of braid groups and their quotients.
method Use algebraic and geometric methods to classify groups and construct fibrations.
result Prove that for groups of order 64, if not 32, then order is at least 64, and classify cases where equality holds.
We characterize the para-associative ternary quasigroups (flocks) applicable to knot theory, and show which of these structures are isomorphic. We enumerate them up to order 64. We note that the operation used in knot-theoretic flocks has its non-associative version in extra loops. We use a group action on the set of f…
New unoriented versions of Schur and Bogomolov multipliers for finite groups.
problem Defining and analyzing unoriented versions of Schur and Bogomolov multipliers.
method Using cohomology groups and quotient groups to define unoriented multipliers.
result Triviality of unoriented Bogomolov multiplier for certain groups, nontriviality for others.
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…
Y. Nikonorov completes a proof in a geometry paper.
problem Completing a proof in a geometry paper.
method Completing an argument from a previous proof.
result Proof of Theorem 2.5 in JGA 27 (2017) is now complete.
The study shows involutory quandles of certain links are not left-orderable.
problem Determining left-orderability of involutory quandles of links.
method Using a non-left-orderability criterion for involutory quandles of non-split links, the study improved previous results and introduced new families of links.
result The involutory quandles of non-trivial alternating links and certain augmented alternating links are not left-orderable.
Study K-theory of homogeneous spaces of Lie groups.
problem Classifying and understanding the topological invariants of homogeneous spaces.
method Apply K-theory to homogeneous spaces of simply connected, compact Lie groups.
result Detailed analysis of four symmetric spaces, revealing their topological properties.
A new optimization method reduces memory and compute requirements for deep learning.
problem Memory and compute constraints in second-order stochastic optimizers for deep learning.
method Proposes KrAD, a novel factorization to approximate inverse Fisher matrix without inversion, leading to KrADagrad.
result Improves performance over Shampoo for 32-bit precision and comparable/generalization on real datasets.
In the description of the instanton Floer homology of a surface times a circle due to Muñoz, we compute the nilpotency degree of the endomorphism u2−64. We then compute the framed instanton homology of a surface times a circle with non-trivial bundle, which is closely related to the kernel of u2−64. We discuss th…
A new sampling method called Restart improves both speed and quality of generative processes.
problem Balancing speed and quality in generative processes involving differential equations.
method Alternates between adding noise and following ODE, improving both speed and quality.
result Surpasses previous SDE and ODE samplers in both speed and accuracy.
We propose a principled method for gradient-based regularization of the critic of GAN-like models trained by adversarially optimizing the kernel of a Maximum Mean Discrepancy (MMD). We show that controlling the gradient of the critic is vital to having a sensible loss function, and devise a method to enforce exact, ana…
Solar improves variable selection in high-dimensional data with complicated dependence structures.
problem Variable selection in ultrahigh dimensional data with severe multicollinearity and grouping effect issues.
method Subsample-ordered least angle regression (Solar) for ultrahigh dimensional data.
result Solar yields substantial improvements in sparsity, stability, and accuracy of variable selection compared to traditional methods.
The paper explores conditions for the existence of orthogonal almost complex structures on manifolds.
problem Conditions for the existence of orthogonal almost complex structures on manifolds.
method Analyzes the Nijenhuis tensor and its squared norm to determine the existence of orthogonal almost complex structures.
result There exists no orthogonal almost complex structure on the standard sphere \(S^6\) with \(|N|^2 < \frac{64}{5}\) everywhere.
SciRE-Solver accelerates DMs sampling by recursively calculating the score function derivative.
problem Slow iterative process of diffusion models due to estimating the score function derivative.
method Recursive Difference (RD) method combined with truncated Taylor expansion of score-integrand.
result SciRE-Solver achieves state-of-the-art FIDs with significantly fewer score function evaluations.
We use Floer's exact triangle to study the u-map (cup product with the 4-dimensional class) in the Floer cohomology groups of admissible SO(3) bundles over closed, oriented 3-manifolds. In the case of non-trivial bundles we show that (u^2-64)^n = 0 for some positive integer n. For homology 3-spheres Y the same holds fo…
James's octonionic Stiefel spaces questions answered partially.
problem Two fundamental questions about octonionic Stiefel spaces.
method Partial answers to James's questions about octonionic Stiefel spaces.
result Partial answers to James's questions about octonionic Stiefel spaces.
We propose studies of special Riemannian geometries with structure groups H1=SO(3)⊂SO(5), H2=SU(3)⊂SO(8), H3=Sp(3)⊂SO(14) and H4=F4⊂SO(26) in respective dimensions 5, 8, 14 and 26. These geometries, have torsionless models with symmetry groups G1=SU(3), $G_2=SU(3)\times SU(3)…
Proposes new methods for Markov chain choice models with panel data.
problem Dependence among transactions for the same customer in historical data.
method Expectation-maximization (EM) algorithms incorporating partial-ordering preference information.
result EM algorithms outperform traditional methods on synthetic and real datasets.
New cube complexes disprove Kalai's conjecture about sphere facets.
problem Disproving Kalai's conjecture about the number of facets of cubical spheres.
method Constructing cube complexes homeomorphic to the d-sphere with n vertices and Ω(n^(5/4)) facets.
result The conjecture is disproved for all d≥3 and n sufficiently large.
Background: Fluctuating hearing loss is characteristic of Meniere's Disease (MD) during acute episodes. However, no reliable audiometric hallmarks are available for counselling the hearing recovery possibility. Aims/Objectives: To find parameters for predicting MD hearing outcomes. Material and Methods: We applied mach…
We developed a convolution neural network (CNN) on semi-regular triangulated meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN, including convolution and down-sampling, are directly defined in a vertex domain. By exploiting the ordering property of semi-regular meshes, the convolution is defin…
Improved Thompson Sampling algorithms for bandits with tighter regret bounds.
problem Efficient and adaptive algorithms for stochastic bandits with bounded rewards.
method Proposed two parameterized Thompson Sampling-based algorithms: TS-MA-α and TS-TD-α.
result Achieved O(Kln^(α+1)(T)/Δ) regret bound, improving scalability and resource allocation.
Generative adversarial networks have been successfully applied to inpainting in natural images. However, the current state-of-the-art models have not yet been widely adopted in the medical imaging domain. In this paper, we investigate the performance of three recently published deep learning based inpainting models: co…
This study uses ARM to analyze pedestrian crashes under different lighting conditions.
problem Identifying crash risk factors under varying lighting conditions.
method Applied Association Rules Mining to Louisiana pedestrian crash data.
result Daylight crashes are associated with children, seniors, and older drivers.
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of…
SeqRF straightens generative model flows to speed up sampling.
problem High global truncation error in ODE-based solvers for generative models.
method SeqRF, a learning technique that straightens the probability flow.
result Significantly improved sampling speed and synthesis quality.
A new sampling method balances multi-label datasets by preserving category frequency order.
problem Sampling challenges in multi-label datasets with varying label frequencies.
method Uses multivariate Bernoulli distribution and label dependencies to estimate and weight label combinations.
result Produces a more balanced sub-sample with enhanced representation of minority categories.
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…
Proves classification of 4D complete intersections up to diffeomorphism.
problem Classifying 4-dimensional complete intersections up to diffeomorphism.
method Uses Hambleton-Madsen theory of degree-d normal maps and connects Segal Conjecture for S1 to Sullivan Conjecture. result Proves the Sullivan Conjecture for 4-dimensional complete intersections.
Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.
problem Characterizing left-orderability in HNN extensions of groups.
method Analyzes HNN extensions of torsion-free nilpotent groups and left-orderable groups.
result Constructs examples of non-left-orderable HNN extensions of left-orderable groups.
We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler-Lagrange equations on the 2nd order tangent group from the 1st order Euler-Lagrange equ…
Paper defines benchmarks for learning new tasks sequentially.
problem Efficient evaluation of continual few-shot learning.
method Theoretical framework and flexible benchmarks.
result Introduction of SlimageNet64 for efficient evaluation.
ARTEMIS combines deep learning and symbolic reasoning for financial predictions.
problem Lack of interpretability and economic principles in deep learning models in finance.
method Neuro-symbolic framework combining neural operators, stochastic differential equations, and symbolic distillation.
result ARTEMIS achieves state-of-the-art directional accuracy, outperforming all baselines on synthetic crash regime.
Improved road segmentation on low-res LIDAR data for autonomous vehicles.
problem Low-resolution LIDAR data affects road segmentation accuracy in autonomous vehicles.
method Subsampled LIDAR data transformation into feature maps, use local normal vector with spherical coordinates.
result Improves road segmentation accuracy on low-resolution LIDAR data.
Enhanced SMC2 uses gradients from CRN-PF in Langevin proposals for improved state and parameter estimation.
problem Challenges in high-dimensional parameter spaces for SMC2. method Leveraging gradients from a CRN-PF within a Langevin proposal.
result Higher effective sample size and more accurate parameter estimates.
Efficiently samples posterior distributions using Langevin dynamics.
problem Challenges in generating diverse posterior samples in high-dimensional spaces.
method Simulates Langevin dynamics in the noise space of a pre-trained generative model.
result Noise-space Langevin dynamics approximates the posterior without restarting the full sampling chain.
The paper constructs Ricci-flat Kähler manifolds with specific decay properties.
problem Finding Ricci-flat Kähler manifolds with controlled decay rates.
method Geometric existence proof and construction of ansatz.
result Existence of 39 distinct Ricci-flat Kähler 3-folds with specific asymptotic angles.
Study of group orderability using tensor and exterior squares.
problem Circular orderability of groups and torsion elements.
method Analysis of tensor and exterior squares of groups.
result Circularly orderable groups have left-orderable tensor and exterior squares under certain conditions.
New criterion for bi-ordering free groups under automorphisms.
problem Bi-ordering free groups under automorphisms.
method New criterion for bi-ordering free groups.
result Fundamental group of the magic manifold is bi-orderable.
In this study an Artificial Neural Network was trained to classify musical instruments, using audio samples transformed to the frequency domain. Different features of the sound, in both time and frequency domain, were analyzed and compared in relation to how much information that could be derived from that limited data…
Tensor factorization has become an increasingly popular approach to knowledge graph completion(KGC), which is the task of automatically predicting missing facts in a knowledge graph. However, even with a simple model like CANDECOMP/PARAFAC(CP) tensor decomposition, KGC on existing knowledge graphs is impractical in res…
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…
Bi-orderable groups from left-orderable ones, showing non-profinite properties.
problem Non-profinite properties in bi-orderability and generalized torsion elements.
method Using fiber products to construct bi-orderable groups, showing non-profinite properties.
result Bi-orderability and generalized torsion elements are not profinite properties.
We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package…
Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a cofinal family) in many separable metric spaces of interest. To get hold on uniform homotopy properties of these spaces, a reasonably behaved notion of an infinite-dimensional metric polyhedron is needed; a specific list of desired properties …
Sample-Rank simplifies MO recommendations by sampling and ranking, improving revenue with stable conversion rates.
problem Multi-objective recommendations in online food ordering systems.
method Multi-goal sampling followed by ranking, reducing MO problem to LTR model.
result Significant lift in revenue (2.64%) with stable conversion rates, no drop in last-mile traversal.
The paper explores circular orderability in 3-manifold groups, related to the L-space conjecture.
problem Circular orderability of 3-manifold groups and its relation to the L-space conjecture.
method Investigation of finite cyclic covers and Dehn surgeries to establish circular orderability.
result Circularly orderable fundamental groups of compact, connected, P^2-irreducible 3-manifolds are characterized.
Study builds non-bi-orderable groups without generalized torsion.
problem Constructing non-bi-orderable groups without generalized torsion.
method Constructing specific one-relator groups.
result Demonstrates existence of non-bi-orderable groups without generalized torsion.