Models predict player motivation from game data.
problem Predict player motivation from gameplay data.
method Collected gameplay data and survey responses, used SVM for inference.
result Models accurately predict player motivation (92%-94%).
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48 results for “Tom Clancy's The Division”
This is a survey of some of the work of Tom Farrell and Lowell Jones. This is the lead article of a special issue of the Pure and Applied Mathematics Quarterly. This issue is published in conjunction with the conference "Geometry,Topology, and their Interactions" held in Morelia, Mexico.
Modeling ToM in multi-agent games using adaptive feedback control.
problem Understanding how agents predict and model other agents' mental states in complex interactions.
method Embodied and situated agent models based on distributed adaptive control theory.
result Probabilistic learning agents outperform pure reinforcement-based strategies in game-theoretic tasks.
Researchers use Gysin sequence to show sl(N) homology of T(2,m) is cohomology of SU(N) representations.
problem Calculating sl(N) homology of T(2,m) explicitly.
method Used Gysin exact sequence to show isomorphism without explicit calculation.
result sl(N) homology of T(2,m) is isomorphic to cohomology of SU(N) representations.
We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.
New map constructed from equivariant spectra for manifold study.
problem Understanding equivariant parametrized h-cobordism in non-manifold settings.
method Constructed a map from suspension G-spectrum to equivariant A-theory spectrum, compatible with tom Dieck splitting formulas.
result Fiber of constructed map is wedge of stable h-cobordism spectra.
Let G be a finite group. The unit sphere in a finite-dimensional orthogonal G-representation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue, and establish its basic properties including the Borel-Smith conditions and realization by finite G-CW-complexes.
Hurd's career overview and publications listed.
problem None explicitly stated in the abstract.
method Not applicable as it's an introduction.
result No specific key result mentioned.
From division to extensionmath.CV
A new proof of an extension theorem with bounded generators.
problem Extension theorems in complex analysis.
method Skoda-type division theorem with bounded generators.
result The new division theorem allows to be 1 in the norm of the datum.
Solves division problem for L. Hörmander's systems.
problem Division problem for L. Hörmander's overdetermined systems.
method Formulates and proves divisibility criterion, coherence theorem.
result Establishes effective divisibility criterion and extends coherence theorem.
Proves divisibility relations for symplectic curve polynomials.
problem Divisibility relations for symplectic curve polynomials.
method New proofs of divisibility relations for Oka and Alexander polynomials of symplectic curves.
result Proves Libgober's divisibility relations for symplectic curves.
Uniform convexity in divisible domains leads to hyperbolic geometry.
problem Understanding the geometry of divisible convex sets in Finsler manifolds.
method Proving -uniform convexity of a specific Finsler metric.
result A strictly convex divisible domain induces a -uniformly convex Finsler metric.
Tropical division approximates polynomial division for neural networks.
problem Approximating polynomial division in max-plus semiring.
method Approximating Newton Polytope of dividend by divisor, then applying to neural networks.
result Minimizes a two-layer fully connected network for binary classification.
Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of -planes in when . Moreover, this convex divisible domain is a model of the symmetric space associ…
We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as Fock-Goncharov coordinates of framed -local systems on a marked bordered surface. Using this result, we show that these Borel sums can be meromorphically continued to any point of $\math…
Division algorithm for surface group rings yields standard complexes and cohomological dimensions.
problem Understanding cohomological dimensions of surface group actions.
method Division algorithm for group rings of surface groups.
result Some 2-complexes with surface fundamental groups are standard.
Adopting a zonal structure of electricity market requires specification of zones' borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational …
This is a survey of our recent work with Tom Mrowka on Seiberg-Witten gauge theory and index theory for manifolds with periodic ends. We explain how this work leads to a new invariant, which is related to the classical Rohlin invariant of homology 3-spheres and to the Furuta-Ohta invariant originating in Yang-Mills gau…
In this paper we provide a detailed proof of the second variation formula, essentially due to Richard Hamilton, Tom Ilmanen and the first author, for Perelman's -entropy. In particular, we correct an error in the stability operator stated in Theorem 6.3 of [2]. Moreover, we obtain a necessary condition for linearly …
Geometrically explains divisibility of Euler classes for spin modules.
problem Divisibility of -theoretical Euler classes for spin modules.
method Geometric interpretation of divisibility using spin structures and Seiberg-Witten theory.
result Clarifies the role of reducibles in monopole equations.
New proof of divisibility property for certain algebraic varieties.
problem Divisibility property for LQEL varieties.
method Construction of Clifford algebra representations to Severi varieties.
result New proof of Russo's Divisibility Property for LQEL varieties.
The paper sets lower bounds on envy-free divisions in cake-cutting problems.
problem Finding the minimum number of envy-free divisions in cake-cutting problems.
method Analyzes two scenarios: classical and hybrid, with different constraints and allocations.
result Sharp bounds and examples for envy-free divisions in both scenarios.
The paper revisits Rokhlin's divisibility theorem and its significance.
problem Rokhlin's divisibility theorem on signatures of manifolds.
method Overview and retrace of Rokhlin's proof and further developments.
result Reaffirms the importance of Rokhlin's theorem in manifold theory.
Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.
problem Division Theorem in Skoda's context
method Degeneration approach inspired by B. Berndtsson and L. Lempert's extension theorem
result Simplified and extended proof of extension theorem
Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial bundle, our results recover Skoda's division theorem for holomorphic …
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
problem Understanding the distinction between incidence theorems over division rings and fields.
method Extending the surface-graph approach to noncommutative settings, the paper analyzes the topological properties of graphs embedded on surfaces of different genera.
result Theorems associated with graphs on the sphere hold over any division ring, while those on surfaces of positive genus typically hold only if the ground ring is a field.
Constructs projective plane over octonions, proving no higher real division algebras.
problem Existence of higher-dimensional real division algebras.
method Using Adams' solution of the Hopf invariant 1 problem, constructs projective plane over octonions.
result No higher-dimensional real division algebras exist.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
problem Inferring protein production kinetics in dividing cells due to protein inheritance and division history.
method Adapted conditional normalizing flows to approximate intractable likelihoods from simulated data.
result Glc3 gene is mostly inactive under stress, with brief and transient expression.
Geodesic connectedness proved for statistical manifolds with divisible cubic forms.
problem Geodesic connectedness of affine connections on statistical manifolds with divisible cubic forms.
method Analogy with Hopf-Rinow theorem in Riemannian geometry, establishing geodesic completeness.
result Geodesic connectedness established for statistical manifolds with divisible cubic forms.
New proofs of knot detection using instanton Floer homology.
problem Detecting specific knots using homology theories.
method Using instanton Floer homology instead of knot Floer homology.
result Proves detection of specific knots using instanton homology.
A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which classifies the universal one-dimensional commutative formal group law. We prove an equivariant generalization of this result by identifying the homotopy theoretic -equivariant unitary bordism ring, in…
Study of characteristic numbers in 24-dimensional String manifolds.
problem Characterizing and understanding characteristic numbers of 24-dimensional String manifolds.
method Using Pontryagin numbers, integral basis of String cobordism group, and divisibility results.
result Established 2- and 3-primary divisibilities of characteristic numbers.
Algorithm learns fair division from noisy feedback in uncertain markets.
problem Learning fair division in uncertain markets with noisy feedback.
method Wrapper algorithms using dual averaging to learn item and agent values from bandit feedback.
result Asymptotically achieves optimal Nash social welfare in linear Fisher markets.
An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have boundary, and have word hyperbolic divid…
The Jones polynomial's divisibility is analyzed via local moves on virtual links.
problem Divisibility of the Jones polynomial under local moves on virtual links.
method Developed a general decomposition for the Jones polynomial of virtual links and analyzed divisibility conditions for various local moves.
result Succinct divisibility conditions on the Jones polynomial of virtual links differing via local moves.
In this note we introduce a construction which assigns to an arbitrary manifold bundle its fiberwise orientation covering. This is used to show that the zeta classes of unoriented surface bundles are not divisible in the stable range.
Study shows non-symmetric convex sets have full boundary limits.
problem Understanding boundaries of non-symmetric convex sets.
method Proved using proximal limit set analysis.
result Proximal limit set equals full projective boundary for non-symmetric irreducible divisible convex sets.
Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain tr…
New cohomology theory shows compact Lie group actions are Morita invariant.
problem Establishing Morita invariance for cohomology of compact Lie group actions.
method Using bibundles to transfer coefficient systems between Morita equivalent groupoids.
result Twisted Bredon-Illman cohomology is Morita invariant for compact Lie group actions.
Study of congestion in negative curvature manifolds using fair-division algorithms.
problem Estimating and predicting the size and location of congestion core in negative curvature manifolds.
method Introducing a novel fair-division algorithm to estimate congestion core.
result Demonstrated the effectiveness of fair-division algorithms in estimating congestion core.
Research shows how certain flat structures behave in specific convex domains.
problem Understanding the behavior of codimension-1 simplices in divisible convex domains.
method Analyzes the set of codimension-1 flats and their images in quotient manifolds.
result The set of codimension-1 flats forms a finite collection of disjoint virtual tori, leading to cusped convex projective manifolds.
LLMs can collude in market divisions, maximizing profits.
problem Strategic collusion of LLM agents in multi-commodity markets.
method Examined LLMs in Cournot competition frameworks, analyzing pricing and resource allocation strategies.
result LLMs can monopolize specific commodities without direct human input or explicit collusion commands.
Constructs modular forms and proves divisibility results for odd-dimensional manifolds.
problem Constructing modular forms over specific groups and proving divisibility results.
method SL(2, Z) modular forms and Witten genus in odd dimensions.
result Obtained divisibility results of index of Toeplitz operators on spin and spin^c manifolds.
New invariants from divisibility of Lee classes for slice-torus.
problem Determining slice-torus knots using Lee class divisibility.
method Defined new invariants from divisibility of reduced Lee class invariants.
result New invariants coincide with Rasmussen invariant for certain cases.
In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds admitting several symplectic structures, inequivalent under deformation and sel…
HiPart offers an efficient, interactive tool for hierarchical clustering.
problem Efficient and interpretable hierarchical clustering for Big Data.
method Divisive hierarchical clustering algorithms with interactive visualizations.
result High computational efficiency and interpretability in Big Data applications.
New algorithms for fair item allocation with limited copies.
problem Fair division of numerous items with few copies.
method Modeling as a contextual bandit problem with sub-linear regret guarantees.
result Proposed algorithms achieve sub-linear regret in fair item allocation.