We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic vari…
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48 results for “Minimal Model Program”
The paper shows how certain complex projective varieties can be broken down into simpler types.
problem Understanding the structure of complex projective varieties with pseudo-effective tangent sheaves.
method Developed a theory of pseudo-effective sheaves and applied the minimal model program.
result Projective klt varieties with pseudo-effective tangent sheaves can be decomposed into Fano varieties and Q-abelian varieties.
We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the proof of the ACC conjecture for log canonical thresholds and the recent progress on the `local stability theory' of an arbitrary Kawamata log…
The paper solves a 5-manifold foliation problem using a Sasaki-Ricci flow.
problem Solving foliation singularities on Sasakian 5-manifolds.
method Applying the Sasaki-Ricci flow to resolve cyclic quotient foliation singularities.
result Proves a Sasaki analogue of the analytic minimal model program.
In this note we propose to show that the Kähler-Ricci flow fits naturally within the context of the Minimal Model Program for projective varieties. In particular we show that the flow detects, in finite time, the contraction theorem of any extremal ray and we analyze the singularities of the metric in the case of divis…
The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. We consider the ana…
New algorithms improve submodular minimization via DC programming.
problem Minimizing the difference of two submodular functions.
method Introducing variants of the DC algorithm (DCA) and its complete form (CDCA) for DC programs corresponding to DS minimization.
result Our algorithms outperform existing baselines on speech corpus selection and feature selection.
Efficiently constructs prediction bands with minimal assumptions.
problem Uncertainty quantification for nonparametric, heteroscedastic data.
method Semi-definite programming for data-adaptive prediction bands.
result Strong non-asymptotic coverage properties with minimal distributional assumptions.
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach tur…
In 1960s, Almgren initiated a program to find minimal hypersurfaces in compact manifolds using min-max method. This program was largely advanced by Pitts and Schoen-Simon in 1980s when the manifold has no boundary. In this paper, we finish this program for general compact manifold with nonempty boundary. As a result, w…
In this paper we consider regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer.…
Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recove…
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
The paper certifies decision trees against evasion attacks using program analysis.
problem Vulnerability of decision tree models to evasion attacks by maliciously crafted perturbations.
method Transform decision trees into imperative programs for program analysis, leveraging abstract interpretation.
result Soundly verifies security guarantees of decision tree models, yielding minimal false positives.
Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Informationmath.OC
Paper proposes a new method for SP with covariates using PADR and ERM.
problem Stochastic programming with covariate information.
method Empirical risk minimization (ERM) with nonconvex piecewise affine decision rules (PADR).
result The method provides theoretical consistency and computational tractability for nonconvex SP problems.
In this paper we study the birational geometry of HyperKaehler manifolds by combining the method of minimal model program and the traditional approach of symplectic geometry.
Method estimates dataset utility via minimal program length proxy.
problem Determining if data labels are generated by useful subroutines.
method Rissanen Data Analysis (RDA) estimates minimum description length (MDL) as a proxy.
result Method reveals dataset characteristics and utility in various NLP settings.
We extend the classical risk minimization model with scalar risk measures to the general case of set-valued risk measures. The problem we obtain is a set-valued optimization model and we propose a goal programming-based approach with satisfaction function to obtain a solution which represents the best compromise betwee…
The Kähler-Ricci flow near conical singularities is described with a curvature bound.
problem Describing the Kähler-Ricci flow near conical singularities.
method Showed a curvature bound and used the unique Kähler-Ricci expander.
result The flow near each singular point is modelled on the unique Kähler-Ricci expander.
Unsupervised clustering of series using dynamic programming.
problem Clustering coherent segments in multi-variate series.
method Dynamic programming algorithm with constraints.
result Clusters of coherent segments identified using Waxman-Smits equation.
Max-linear regression problem solved with convex programming.
problem Estimating parameters in max-linear regression models.
method Formulated and analyzed a scalable convex program called anchored regression (AR).
result AR provides high probability recovery of parameters with a sample complexity of .
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With random measurements of a positive semidefinite matrix of rank and condition number …
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
Optimizes intervention design for causal discovery using integer programming.
problem Identifying causal structures from observational data due to confounding variables.
method Uses integer programming to design minimal intervention sets for causal structure identifiability.
result Provides exact and modular solutions adaptable to various experimental settings and constraints.
Linear time dynamic programming for the exact path of optimal models selected from a finite setcs.LG
New algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
In this paper we prove the existence of rational homology balls smoothly embedded in regular neighborhoods of certain linear chains of smooth -spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.
A Natural Copulaq-fin.RM
A new copula minimizes distance between distributions.
problem Arbitrariness in copula choice.
method Minimizes Wasserstein distance; linear programming estimation.
result Natural copula provides parsimonious estimation.
The problem of automatic software generation is known as Machine Programming. In this work, we propose a framework based on genetic algorithms to solve this problem. Although genetic algorithms have been used successfully for many problems, one criticism is that hand-crafting its fitness function, the test that aims to…
Paper aims to minimize ruin probability in insurance companies using Sparre Andersen model.
problem Minimizing ruin probability in insurance companies with Sparre Andersen surplus process.
method Markovization of the surplus process, investigation of value function's regularity, dynamic programming principle, and comparison of viscosity solutions.
result The value function is the unique constrained viscosity solution to the Hamilton-Jacobi-Bellman equation.
We consider the problem of tracking a target whose dynamics is modeled by a continuous Itō semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be relat…
Sharp condition found for Burer-Monteiro method to work for MaxCut-type SDPs.
problem MaxCut-type semidefinite programs with low-rank solutions.
method Sharp condition on Laplacian matrix conditioning for global minimizers of non-convex problem.
result Any second-order critical point is a global minimizer under the given condition.
We describe an approximate dynamic programming (ADP) approach to compute approximations of the optimal strategies and of the minimal losses that can be guaranteed in discounted repeated games with vector-valued losses. Such games prominently arise in the analysis of regret in repeated decision-making in adversarial env…
Paper proves structure of compact Kähler 3-folds with specific bundles.
problem Characterizing compact Kähler 3-folds with nef anti-canonical bundles.
method Minimal Model Program, positivity of direct image sheaves, Q-conic bundles, orbifold vector bundles.
result Compact Kähler 3-folds with nef anti-canonical bundles are essentially one of three types.
Study minimal solutions to a reflected process driven by jump processes.
problem Ruin time of interconnected insurance firms.
method Minimal strong solution to a particle system with a linear programming problem.
result Existence of a unique stopping time for the ruin process.
Regulator allocates buffers to prevent financial contagion in networks with common assets.
problem Containment of default contagion in financial networks with common asset exposures.
method Allocates nonnegative buffer vectors under linear budget constraints to maximize default or insolvency resilience margins or minimize worst-case systemic losses.
result Exact synthesis results for buffer allocation under and uncertainty sets, showing significant gains over uniform and exposure-proportional allocations.
A new method for 3D surface registration using dynamic programming.
problem Elastic shape registration of 3D surfaces.
method Optimization over a subset of reparametrizations using dynamic programming.
result Proposes an algorithm that produces a solution closer to optimal than gradient-based methods.
This research optimizes Andrews plots for better visual clarity in high-dimensional data.
problem Visualizing high-dimensional datasets with clarity and aesthetics.
method Developed a method to add spectral smoothing to Andrews plots to reduce visual clutter.
result Optimal spatial-spectral smoothing leads to more aesthetically pleasing and clutter-free visualizations.
A new method detects changes in machine learning models over time.
problem Automatic monitoring of machine learning models trained on evolving data.
method Score-based statistical hypothesis test for change detection.
result The method can detect changes in any number of model components.
We present computational results about quasi-alternating knots and links and odd homology obtained by looking at link families in the Conway notation. More precisely, we list quasi-alternating links up to 12 crossings and the first examples of quasi-alternating knots and links with at least two different minimal diagra…
We prove the existence of global minimizers of Allen-Cahn equation in dimensions and above. More precisely, given any strictly area-minimizing Lawson's cones, there are global minimizers whose nodal sets are asymptotic to the cones. As a consequence of Jerison-Monneau's program we establish the existence of many co…
Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is necessarily of log general type. Given a quasi-projective threefold Y that admits a no…
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are me…
New method detects changes by maximizing cross-entropy, outperforming existing techniques.
problem Detecting abrupt changes in data streams without labeled examples.
method Maximizes cross-entropy between segments to find change points, using dynamic programming.
result Outperforms three state-of-the-art approaches on challenging datasets.
Most of the existing methods for sparse signal recovery assume a static system: the unknown signal is a finite-length vector for which a fixed set of linear measurements and a sparse representation basis are available and an L1-norm minimization program is solved for the reconstruction. However, the same representation…
We use a new combinatorial technique to prove the optimal interior partial regularity result for Lp-vectorfields with integer fluxes minimizing the Lp-energy. More precisely, we prove that the minimal vectorfields are Hölder outside a set which is locally finite inside the domain. The results continue the program start…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming models for regression subset selection based on mean square and absolute errors…
The paper analyzes financial networks with default charges and defines a model using fixpoint problems.
problem Modeling systemic risk in interbank networks with crossholdings and default charges.
method Mixed integer-linear programming and Gaussian elimination algorithm for computing clearing pairs.
result Developed methods to compute maximal and minimal clearing pairs.
To save manual effort, developers often translate programs from one programming language to another, instead of implementing it from scratch. Translating application program interfaces (APIs) used in one language to functionally equivalent ones available in another language is an important aspect of program translation…