Related papers: An exact lower bound within a 331 model closing so…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a…
In this note we address the relation between symbolic and ordinary powers of the ideal of a reduced set or points in projective space: the so-called containment problem. In particular, we obtain sharp lower bounds on the Waldschmidt…
We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
This study finds exact closed-form solutions for compensating variation (CV) and equivalent variation (EV) for both marginal and non-marginal changes in public goods given homothetic, but non-separable, utility where a single sufficient…
We consider a class of discretionary stopping problems within the $G$-framework. We first establish the well-definedness of the stopping problem under the $G$-expectation, by showing the quasi-continuity of the stopped process. We then…
We revisit the stability of the Standard Model vacuum, and investigate its quantum effective potential using the highest available orders in perturbation theory and the most accurate determination of input parameters to date. We observe…
We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the most flexible degrees of freedom. This Slow-Fast Decomposition (SFD) enslaves exponentially…
We study constraints to avoid deep unrealistic minima in the next-to-minimal supersymmetric standard model. We analyze a scalar potential along directions where all of and one of the three Higgs fields develop their vacuum expectation…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
This work aims to provide a comprehensive and unified numerical analysis for non linear system of parabolic variational inequalities (PVIs) subject to Dirichlet boundary condition. This analysis enables us to establish an existence of the…
We consider equations of the form $\Delta u +\lambda^2 V(x)e^{\,u}=\rho$ in various two dimensional settings. We assume that $V>0$ is a given function, $\lambda>0$ is a small parameter and $\rho=\mathcal O(1)$ or $\rho\to +\infty$ as…
We examine the gauge dependence of lower bounds on the Higgs mass obtained from the requirement that the electroweak vacuum be the global minimum of the effective potential. We study a simple model, the spontaneously-broken Abelian Higgs…
The stability of the Standard Model is determined by the true minimum of the effective Higgs potential. We show that the potential at its minimum when computed by the traditional method is strongly dependent on the gauge parameter. It…
It appears difficult to construct a simple model for an open universe based on the one bubble inflationary scenario. The reason is that one needs a large mass to avoid the tunneling via the Hawking Moss solution and a small mass for…
We argue that the following three statements cannot all be true: (i) our vacuum is a type IIB / F-theory vacuum at moderate-to-large $h^{1,1}$, (ii) the $\alpha'$-expansion is controlled via the supergravity approximation, \`a la the KKLT…
We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller's expected revenue is $1/e$ times the geometric…
The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…
Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of…
We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct…