The study examines six variations of apex graphs and their planar properties.
problem Characterizing apex, edge apex, and contraction apex graphs.
method Defined and analyzed six variations of apex graphs, using the Graph Minor Theorem and determining obstruction graphs.
result Found at least 36, 55, and 82 obstruction graphs for apex, edge apex, and contraction apex respectively.
A simpler proof for apex graphs in McCarty and Thomas' conjecture.
problem Proving a conjecture about apex graphs and their linklessly embeddable properties.
method Shorter and simpler proof for the apex case.
result A shorter and simpler proof for the apex case of the conjecture.
A graph is 2-apex if it is planar after the deletion of at most two vertices. Such graphs are not intrinsically knotted, IK. We investigate the converse, does not IK imply 2-apex? We determine the simplest possible counterexample, a graph on nine vertices and 21 edges that is neither IK nor 2-apex. In the process, we s…
New proof for graphs with 21 edges not 2-apex.
problem Identifying graphs with 21 edges that are not 2-apex.
method Combination of triangle-Y and Y-triangle moves on K7, proving minor minimal properties.
result The 20 Heawood family and 7 Petersen family are minor minimal for not 2-apex and not apex properties.
A three-dimensional orthoscheme is defined as a tetrahedron whose base is a right-angled triangle and an edge joining the apex and a non-right-angled vertex is perpendicular to the base. A generalization, called complete orthoschemes, of orthoschemes is known in hyperbolic geometry. Roughly speaking, complete orthosche…
We show that the 14 graphs obtained by ∇Y moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of ∇Y and Y∇ mo…
Most graphs are knotted as they grow larger.
problem Understanding the prevalence of knotting in random graphs as they increase in size.
method Four models for random graphs were analyzed to determine the probability of intrinsic knotting.
result The probability of a graph being intrinsically knotted approaches 1 as the number of vertices increases.
New constructions from non-separating planar graphs improve understanding of graph linkability and knotability.
problem Understanding linkability and knotability of graph complements.
method Using maximal non-separating planar graphs to construct examples of maximal linkless and knotless graphs, and analyzing their Colin de Verdière invariant.
result The Colin de Verdière invariant of the complement of a maximal non-separating planar graph satisfies μ(cG) ≤ n-4, and equality holds.
Study hyperbolic 2-spheres with cone points, describing spaces for n=3.
problem Characterize the space of hyperbolic 2-spheres with cone points.
method Analyzing the space C(a0,a1,…,an) for n=3 and n=4. result Detailed description of spaces for n=3 and examples for n=4. The paper proves Schauder estimates on cone products and characterizes harmonic functions.
problem Proving Schauder estimates for metric products of cones.
method Characterizing harmonic functions and using local approximations to measure Hölder continuity.
result Interior Schauder estimates for the Laplacian on cone products are proven.
The abstract discusses smoothing and non-smoothing effects using a metric transformation.
problem Analyzing smoothing and non-smoothing effects in metric measure spaces.
method A transformation of metric measure spaces using the length distance induced by heat kernel measures.
result The transformation smooths some Euclidean cones but not the Heisenberg group.
Continuous metrics on ample bundles lie in infinite-dimensional cones.
problem Understanding the structure of positive metrics on ample line bundles.
method Analyzing bounded graded filtrations and embedding into Mabuchi-flat cones.
result Continuous metrics embed isometrically into the space of positive metrics.
The paper explores coalescent contractions in contractible spaces, providing criteria and examples.
problem Existence and absence of coalescent contractions in contractible spaces.
method Analysis of contractible finite simplicial complexes and criteria for coalescent contractions.
result Criteria for contractible finite simplicial complexes that ensure no coalescent contractions.
Computable contracts simplify financial transactions and reduce legal costs.
problem Difficulty in querying, executing, and analyzing text-based financial contracts.
method Develop a Contract Definition Language and illustrate use cases.
result Substantial improvements in customer experience and cost reduction.
We prove optimal mechanisms for general contract spaces.
problem Optimal mechanism design under adverse selection and ambiguity.
method Existence proof for optimal mechanisms in general contract spaces.
result Centralized contracting is equivalent to delegated contracting.
In an online contract selection problem there is a seller which offers a set of contracts to sequentially arriving buyers whose types are drawn from an unknown distribution. If there exists a profitable contract for the buyer in the offered set, i.e., a contract with payoff higher than the payoff of not accepting any c…
Optimal execution strategy for merger & acquisition contracts with price impact.
problem Optimal execution and pricing of financial derivatives in M&A deals.
method Indifference utility arguments, considering linear and nonlinear contracts.
result Linear contracts are more expensive and vulnerable to manipulation.
The paper proves that a specific type of union of contractible sets is contractible.
problem Whether a union of contractible sets is itself contractible.
method Examined a monotone union of contractible open sets in normal spaces, proving contractibility under certain conditions.
result A normal space X is contractible if it is the union of an increasing sequence of open sets where each contracts to a point in the next.
This paper develops a method to select a reference contract for multi-contract quoting to minimize execution risk.
problem Minimizing execution risk in multi-contract quoting sequences.
method Develops a diagnostic framework using order-flow Hawkes forecasts and CLF to select a stable reference contract.
result Event-history and LOB-state signals offer complementary views for reference-contract selection.
Proposes a probabilistic framework for smart contract risk quantification.
problem Quantifying financial risk of smart contract cyber attacks and failures.
method Probabilistic graph-theoretical framework using bond percolation models.
result Analytical results and numerical examples for aggregate loss distribution.
Complexes' contractibility depends on the Collatz conjecture.
problem Determining contractibility of complex structures.
method Construction of complex structures and analysis of their contractibility.
result Contractibility of complex structures is linked to the Collatz conjecture.
Injectivity of fundamental group map proves contractibility of intersection in CAT(0) complexes.
problem Proving contractibility of intersections of subcomplexes in non-positively curved 2-complexes.
method Injectivity of the induced map from fundamental groups.
result Each component in the intersection of two contractible subcomplexes in a CAT(0) 2-complex is contractible.
Improved security of smart contracts by classifying them into four categories.
problem Detecting and classifying vulnerabilities in smart contracts efficiently.
method Used AWD-LSTM for multi-class classification, addressing class imbalance.
result Achieved a weighted average Fbeta score of 90.0%.
The paper finds optimal insurance contracts in behavioral finance, avoiding moral hazard.
problem Finding optimal insurance contracts that avoid moral hazard in a behavioral finance framework.
method Formulated as a non-concave maximization problem involving Choquet expectation, then solved using calculus of variations.
result Optimal contracts are found for certain values of safety loading, with some contracts never optimal for others.
Study on contracting maps and their rigidity under curvature constraints.
problem Rigidity of contracting maps between manifolds with positive curvature.
method Analysis of curvature pinching and contracting conditions involving singular values.
result Established the relation between curvature pinching and contracting conditions.
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…
Methodology projects forward electricity contract prices using market equilibrium and social welfare optimization.
problem Quantifying forward contract risks and optimizing revenue/cost for generators/load/traders.
method Market equilibrium and social welfare optimization; linear programming for total agents' welfare.
result Equilibrium contract price corresponds to the dual variable of equilibrium constraints.
Study shows some contractible complexes can't have certain immersions.
problem Understanding non-positive immersions in contractible complexes.
method Provided counterexamples to a conjecture by Wise.
result Some contractible complexes do not have non-positive immersions.
The simplicial volume of non-R^3 contractible 3-manifolds is infinite.
problem Characterizing contractible 3-manifolds based on their simplicial volume.
method Analyzing the simplicial volume of contractible 3-manifolds and open 3-manifolds.
result The Euclidean space is the unique contractible 3-manifold with vanishing minimal volume.
Study on reinsurance decisions using mean-variance criterion with irreversible contracts.
problem Optimizing reinsurance premiums and contracts in a Stackelberg game with irreversible contracts.
method Unified singular control framework applied to both discrete and continuous time reinsurance contracts.
result A single once-for-all reinsurance contract is preferred over multiple contracts, and the signing time is crucial.
Optimal contracts help principals delegate data collection in decentralized ML.
problem Dealing with information asymmetries in decentralized ML.
method Design of optimal and near-optimal contracts addressing uncertainty in model quality and performance.
result Simple linear contracts achieve 1-1/e fraction of optimal utility.
Fair insurance contracts are designed to handle default risk using cooperative game theory.
problem Designing fair insurance contracts in the presence of default risk.
method Cooperative game theory to specify premiums and participation in benefit.
result Fair benefit participation emerges as a game outcome involving residual risks.
Optimal contracts are found for agents with quadratic effort costs.
problem Finding optimal contracts in principal-agent problems with quadratic effort costs.
method Modeling the problem using Hamilton-Jacobi-Bellman (HJB) equations and proving the existence of classical solutions.
result Existence of optimal contracts for agents with quadratic effort costs is proven.
Regular languages describe contracting geodesics in groups.
problem Characterizing groups with infinite contracting geodesics.
method Analyzing geodesics in Cayley graphs with a contracting property.
result Groups with infinite contracting geodesics are either virtually Z or acylindrically hyperbolic.
Paper proposes machine learning for managing complex buyback contracts.
problem Managing complex buyback contracts, especially accelerated share repurchase.
method Proposes a machine learning method to optimally manage buyback contracts.
result Recovery of strategies similar to those obtained with partial differential equations and tree methods, but without the curse of dimensionality.
One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytop…
New mortgage contracts reduce underwater default by adjusting loan balances, but must balance prepayment incentives.
problem Underwater default incentives in mortgages.
method Analyzes automatic balance adjustment and prepayment penalties in mortgage contracts.
result Automatic balance adjustments are preferable to traditional contracts at certain spreads, reducing underwater default.
We simplify complex geometric structures for contracting measurable systems.
problem Normal forms for contracting measurable cocycles and foliations.
method Differential-geometric approach to obtain resonance polynomial normal forms via Cq changes of coordinates. result Obtained nonstationary invariant differential-geometric structures for contracting systems and foliations.
Proves measure contraction for specific sub-Riemannian structures.
problem Measure contraction properties in sub-Riemannian structures.
method Analytic sub-Riemannian structures and Lipschitz Carnot groups.
result Proves measure contraction properties for the structures.
We define a new notion of contracting element of a group and we show that contracting elements coincide with hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, rank one isometries in groups acting properly on proper CAT(0) spaces, elements acting hyperbolically on the Bass-Serr…
Groups can embed uniformly but not act properly on contractible manifolds.
problem Understanding the difference between group actions and embeddings on contractible manifolds.
method Analyzing the relationship between group actions and uniform embeddings on contractible manifolds.
result k-fold products of specific groups do not act on contractible manifolds.
Paper presents LLM-enhanced contract metadata extraction.
problem Automatic detection and annotation of legal clauses in contracts.
method Integration of publicly available and proprietary datasets with advanced LLM methodologies.
result Substantial improvements in clause identification accuracy and efficiency.
Optimal linear contracts are possible even with memory in Gaussian settings.
problem Can optimal dynamic contracts be linear when agents control memory processes?
method Developed a methodology for non-Markovian and non-semimartingale settings, showed linear contracts are optimal for one-dimensional models.
result Linear contracts are optimal for one-dimensional models with memory, and for radial effort cost functions in higher dimensions.
Corrects a false claim about a digital sphere model's contractibility.
problem Incorrect claim about MSS_18's 18-contractibility.
method Analyzes digital image MSS_18 as a digital model of S^2.
result Shows MSS_18 is 18-contractible.
RFCN improves cardiac MRI segmentation by leveraging inter-slice spatial correlations.
problem Improving cardiac MRI segmentation accuracy and efficiency.
method Recurrent fully convolutional neural network (RFCN) that learns from full stack of slices.
result RFCN produces state-of-the-art results, improving contour delineation near heart apex.
New contractions found between hyperbolic orbifolds.
problem Finding strict contractions between hyperbolic orbifolds.
method Elementary construction and use of Gueritaud-Kassel and Tholozan's work.
result Exotic quotients of SO_0(d,1) determined.
Combines proportional and stop-loss reinsurance for insurer and reinsurer.
problem Addressing conflicting interests between insurer and reinsurer.
method Introduces proportional-stop-loss reinsurance using balanced loss function.
result Maximizes expected surplus for both insurer and reinsurer.
Algorithm learns optimal contracts for unaware principals.
problem Learning optimal contracts when principal is unaware of agent's utility and action space.
method Sequential contract offers with observed outcomes, using algorithm to approximate optimal contract.
result Algorithm learns optimal contract within epsilon of optimal net profit with bounded samples.