Researchers found a regular language for maximal lexicographic representatives in braid monoids.
problem Understanding the language of maximal lexicographic representatives in braid monoids.
method Detailed description of the smallest Finite State Automaton and analysis of the proportion of elements.
result The proportion of elements of length k whose maximal lexicographic representative finishes with the first generator tends to a number P_{n,1} ≥ 1/8 as k tends to infinity.
The paper proposes a method to infer multi-objective rewards from preferences.
problem Modeling preferences based on multiple, often competing objectives.
method Modeling priorities lexicographically and inferring multi-objective rewards from observed preferences.
result Lexicographically-ordered rewards provide a better understanding of preferences and improve policies.
The paper tackles lexicographic multiarmed bandit problems with bounded regret.
problem Selecting lexicographic optimal arms in multiobjective bandit problems.
method Defining lexicographic regret, considering prior information, and proposing algorithms for both settings.
result Achieves uniformly bounded regret in time for both prior settings and sublinear gap-free regret in the prior-free case.
We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [KP10] and [BKP14]. We also give a sharp…
We study the degree of polynomial representations of knots. We give the lexicographic degree of all two-bridge knots with 11 or fewer crossings. First, we estimate the total degree of a lexicographic parametrisation of such a knot. This allows us to transform this problem into a study of real algebraic trigonal plane c…
We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which allows for infinitely many lexicographically ordered levels of events and for eve…
A new algorithm Zeus for multi-objective clustering with lexicographic ordering and slack.
problem Improving clustering quality with lexicographic objectives and slack.
method Introduced a slack mechanism and proposed Zeus algorithm to solve multi-objective clustering problems.
result Empirical validation of Zeus on real-world data demonstrates its effectiveness.
New fairness concept extends minimax fairness to lexicographic fairness.
problem Fairness in supervised learning, especially lexicographic fairness.
method Introduced approximate lexifairness, derived algorithms for finding solutions, and proved generalization bounds.
result Proved that approximate lexifairness on training data implies approximate lexifairness on true distribution.
Let N and P be smooth closed manifolds of dimensions n and p respectively. Given a Thom-Boardman symbol I, a smooth map f:N→P is called an ΩI-regular map if and only if the Thom-Boardman symbol of each singular point of f is not greater than I in the lexicographic order. We will represent the gr…
The heights of Alexandroff square transformation groups are computed and proven.
problem Computing possible heights of Alexandroff square transformation groups.
method Analyzing the heights of transformation groups for Alexandroff square, unit square with lexicographic order, and unit square with Euclidean topology.
result Proven heights for transformation groups of Alexandroff square, unit square with lexicographic order, and unit square with Euclidean topology.
New connection found between shape reconstruction methods and persistent homology.
problem Connecting shape reconstruction methods with persistent homology.
method Wrap complexes and lexicographic optimal homologous cycles.
result Lexicographically optimal homologous cycles are supported on Wrap complexes.
The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X. We show that the finite subset …
Study how regularization and optimization affect margin in deep models.
problem Understanding margin maximization in deep learning models.
method Analyze the limit of loss minimization with diverging norm constraints and margin paths.
result Discovers lexicographic max-margin solutions for homogeneous models and shows convergence under certain conditions.
Let N and P be smooth manifolds of dimensions n and p (n>=p>=2). Let Omega^{I}(N,P) denote an open subspace of J(N,P) which consists of all Boardman submanifolds Sigma^{J}(N,P) with J=< I in the lexicographic order. We will prove the homotopy principle in the existence level for Omega^{I}(N,P).
New theory for nonsmooth systems helps optimize and control complex functions.
problem Optimizing and controlling systems with nonsmooth functions.
method Higher-order averaging theory with nonsmooth near-identity transformation and lexicographic differentiation.
result Closed formula for nonsmooth first and second-order averaging.
Groups with specific curvature have a regular language of geodesics.
problem Understanding the language of geodesics in non-positively curved triangle groups.
method Proving finitely many cone types and regularity of geodesic languages.
result The language of lexicographically first geodesics is regular and satisfies the fellow traveller property.
DFL framework improves action and outcome fairness in policy learning.
problem Fairness in policy learning, especially action and outcome fairness.
method Integrates action and outcome fairness into a multi-objective optimization problem using a lexicographic weighted Tchebyshev method.
result DFL framework improves both action and outcome fairness with minimal value reduction.
Proof shows imitation of expert's reward and solutions in multi-objective optimization.
problem Multi-objective optimization with reward and solution imitation.
method Wasserstein inverse reinforcement learning.
result Wasserstein inverse reinforcement learning enables imitation of expert's reward and solutions in multi-objective optimization.
We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position…
New method allows backtesting of systemic risk forecasts.
problem Systemic risk measures are not elitable and identifiable, making backtesting impossible.
method Introduces multi-objective elicitability and Diebold--Mariano type tests.
result Proposes a traffic-light approach for backtesting.
New method calculates growth rates of Artin-Tits monoids, linking to partial theta function.
problem Growth rates of Artin-Tits monoids and their connection to partial theta function.
method Determining growth functions using simple matrix determinants and atomic generators.
result Exponential growth rates of Artin-Tits monoids of type An tend to 3.233636... as n increases. The study explores properties and mutations in oriented matroids, proving new results on Euclidean and non-Euclidean structures.
problem Investigating the Euclidean and non-Euclidean properties of oriented matroids.
method Analyzing the minimum number of mutations, using lexicographic extensions, and mutation-flips to prove properties.
result For rank 4 uniform oriented matroids, the minimum number of mutations adjacent to an element is at most 3.
Study a specific line arrangement and compute its fundamental group via braid monodromy.
problem Compute the fundamental group of a specific line arrangement's complement.
method Use braid monodromy to compute the fundamental group.
result The resulting presentation of the fundamental group coincides with the modified Artin presentation.
Deep learning agent improves pedestrian navigation in urban environments.
problem Autonomous driving among pedestrians in urban areas.
method Multi-objective deep reinforcement learning using a deep Q-learning variant.
result The multi-objective DQN agent outperforms single-objective DQN in various environments.
Given a compact geodesic space X we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of X to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their preci…
Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic l1-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexe…
Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the homological density of one space in another. We use Weil's number field/ function field analogy to predict coincidences for limiting homological densities of various sequences $\mathcal{Z}^{(d_1,\…
The paper finds formulas for word lengths and conjugacy classes in surface groups.
problem Finding formulas for word lengths and conjugacy classes in surface groups.
method Investigating symmetric presentations and normal forms of conjugacy classes.
result Derives three formulae for word lengths and provides efficient algorithms for conjugacy problems.
This work tackles asymmetric community estimation in multi-layer directed networks.
problem Estimating different numbers of sender and receiver communities in multi-layer directed networks.
method Proposes a goodness-of-fit test based on the largest singular value of an aggregated normalized residual matrix.
result Develops sequential and ratio-based testing procedures to consistently determine true sender and receiver community numbers.
New RL algorithm ensures stable, replicable policies.
problem Stability and replicability issues in RL algorithms.
method Introduced weak and strong forms of list replicability, developed a novel planning strategy, and tested state reachability.
result Proved efficient tabular RL algorithm with polynomial list complexity.
This paper reviews and introduces measures for data representativity in AI systems.
problem Ensuring appropriate inference from data in AI systems.
method Defined and evaluated three measurable concepts of representativity.
result Contrasts between coverage and distribution representativity are crucial for AI system building.
After defining reduced minimum braid word and criteria for a braid family representative, different braid family representatives are derived, and a correspondence between them and families of knots and links given in Conway notation is established.
After a review of several methods designed to produce equivariant cohomology classes, we apply one introduced by Berline, Getzler and Vergne, to get a family of representatives of the universal Thom class of a vector bundle. Surprisingly, this family does not contain the representative given by Mathaï and Quillen. Howe…
The paper introduces group-representative clustering to ensure fair representation of different groups in clusters.
problem Ensuring fair representation of different groups in clusters.
method Developed a new clustering approach called group-representative clustering, which parallels fairness notions in classification.
result Presented approximation algorithms for group representative k-median clustering and evaluated on real-world data. Study harmonic representatives and cohomology of Oeljeklaus-Toma manifolds.
problem Dolbeault and Bott-Chern cohomology of Oeljeklaus-Toma manifolds.
method Explicit harmonic representatives and geometric analysis.
result Showed geometric Dolbeault formality and studied Angella-Tomassini inequality.
Optimizes sample weights for representative data averages.
problem Achieving sample averages close to prescribed values.
method Formulates as an optimization problem, often convex and efficiently solvable.
result Heuristic methods based on convex optimization perform well.
As previously known, all 3-manifolds of genus two can be represented by edge-coloured graphs uniquely defined by 6-tuples of integers satisfying simple conditions. The present paper describes an ``elementary transformation'' on these 6-tuples which changes the associated graph but does not change the represented manifo…
In the present paper, we will show that a (p,q,r)-pretzel knot has the representativity 3 if and only if (p,q,r) is either ±(−2,3,3) or ±(−2,3,5). We also show that a large algebraic knot has the representativity less than or equal to 3.
A new hierarchical clustering method selects representative points from sub-minimum-spanning-trees.
problem Selecting representative points for hierarchical clustering to improve robustness and reliability.
method Identify representative points using reciprocal nearest data points in sub-minimum-spanning-trees.
result The proposed algorithm outperforms other methods in accuracy and efficiency.
The paper tackles sampling biases by ensuring minority groups are adequately represented in training data.
problem Sampling biases in training data lead to algorithmic biases in machine learning systems.
method The paper presents adaptive sampling methods to determine if it's possible to assemble a representative dataset from given data sources.
result The methods presented can determine with high confidence if a representative dataset can be assembled from given data sources.
For SU(2) (or SO(3)) Donaldson theory on a 4-manifold X, we construct a simple geometric representative for μ of a point. Let p be a generic point in X. Then the set {[A]∣FA−(p) is reducible }, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.
A novel method for estimating group-representative functional networks from multi-subject fMRI data.
problem Estimating common neuronal characteristics in a population from multi-subject fMRI data.
method Two-phase approach: clustering-based ICA for component maps, MAP-MRF labeling for group-representative map estimation.
result Demonstrated the viability of the proposed method in extracting group-representative functional networks from simulated fMRI data.
New Legendrian bounds for non-fibered knots in 3-manifolds.
problem Understanding Legendrian representatives of non-fibered knots.
method Analyzing Thurston-Bennequin bounds and contact invariants.
result Non-fibered knots have Legendrian representatives with tb=0. In an n-manifold X each element of Hn−1(X;Z2) can be represented by an embedded codimension-1 submanifold. Hence for any two such submanifolds there is a third one that represents the sum of their homology classes. We construct such a representative explicitly. We describe the analogous construction…
We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.
We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A …
MOSAIC selects few informative exemplars from high-dimensional data with non-linear structures.
problem Representative selection from high-dimensional data with non-linear structures.
method MOSAIC uses a multi-criteria approach with a quadratic formulation to maximize global representation power, diversity, and outlier detection.
result MOSAIC maximizes data coverage in a transformed space and achieves robustness to various outlier types.
New flows represent Thurston norm ball faces, differing by veering mutations.
problem Dynamic representation of Thurston norm ball faces by distinct flows.
method Combining veering triangulations and mutations to represent faces by multiple flows.
result Non-fibered faces can be represented by two distinct flows differing by veering mutations.