2,254 research outputs found
Robust optimization utilizing the second-order design sensitivity information
This paper presents an effective methodology for robust optimization of electromagnetic devices. To achieve the goal, the method improves the robustness of the minimum of the objective function chosen as a design solution by minimizing the second-order sensitivity information, called a gradient index (GI) and defined by a function of gradients of performance functions with respect to uncertain variables. The constraint feasibility is also enhanced by adding a GI corresponding to the constraint value. The distinctive feature of the method is that it requires neither statistical information on design variables nor calculation of the performance reliability during the robust optimization process. The validity of the proposed method is tested with the TEAM Workshop Problem 2
Contextual Linear Bandits under Noisy Features: Towards Bayesian Oracles
We study contextual linear bandit problems under uncertainty on features;
they are noisy with missing entries. To address the challenges from the noise,
we analyze Bayesian oracles given observed noisy features. Our Bayesian
analysis finds that the optimal hypothesis can be far from the underlying
realizability function, depending on noise characteristics, which is highly
non-intuitive and does not occur for classical noiseless setups. This implies
that classical approaches cannot guarantee a non-trivial regret bound. We thus
propose an algorithm aiming at the Bayesian oracle from observed information
under this model, achieving regret bound with respect to
feature dimension and time horizon . We demonstrate the proposed
algorithm using synthetic and real-world datasets.Comment: 30 page
The projective cover of tableau-cyclic indecomposable -modules
Let be a composition of and a permutation in
. This paper concerns the projective covers of
-modules , and
, which categorify the dual immaculate
quasisymmetric function, the extended Schur function, and the quasisymmetric
Schur function when is the identity, respectively. First, we show that
the projective cover of is the projective indecomposable
module due to Norton, and and the -twist
of the canonical submodule of
for 's satisfying suitable
conditions appear as -homomorphic images of .
Second, we introduce a combinatorial model for the -twist of
and derive a series of surjections starting from
to the -twist of
. Finally, we construct the projective
cover of every indecomposable direct summand of
. As a byproduct, we give a characterization of
triples such that the projective cover of
is indecomposable.Comment: 41 page
Homological properties of 0-Hecke modules for dual immaculate quasisymmetric functions
Let be a nonnegative integer. For each composition of , Berg
introduced a cyclic indecomposable -module
with a dual immaculate quasisymmetric function as the
image of the quasisymmetric characteristic. In this paper, we study
's from the homological viewpoint. To be precise, we
construct a minimal projective presentation of and a
minimal injective presentation of as well. Using them, we
compute and , where is
the simple -module attached to a composition of . We also
compute when
and , where represents the lexicographic
order on compositions.Comment: 44 pages, to be published in Forum of Math: Sigm
DreamStyler: Paint by Style Inversion with Text-to-Image Diffusion Models
Recent progresses in large-scale text-to-image models have yielded remarkable
accomplishments, finding various applications in art domain. However,
expressing unique characteristics of an artwork (e.g. brushwork, colortone, or
composition) with text prompts alone may encounter limitations due to the
inherent constraints of verbal description. To this end, we introduce
DreamStyler, a novel framework designed for artistic image synthesis,
proficient in both text-to-image synthesis and style transfer. DreamStyler
optimizes a multi-stage textual embedding with a context-aware text prompt,
resulting in prominent image quality. In addition, with content and style
guidance, DreamStyler exhibits flexibility to accommodate a range of style
references. Experimental results demonstrate its superior performance across
multiple scenarios, suggesting its promising potential in artistic product
creation
Gaussian Quantum Illumination via Monotone Metrics
Quantum illumination is to discern the presence or absence of a low
reflectivity target, where the error probability decays exponentially in the
number of copies used. When the target reflectivity is small so that it is hard
to distinguish target presence or absence, the exponential decay constant falls
into a class of objects called monotone metrics. We evaluate monotone metrics
restricted to Gaussian states in terms of first-order moments and covariance
matrix. Under the assumption of a low reflectivity target, we explicitly derive
analytic formulae for decay constant of an arbitrary Gaussian input state.
Especially, in the limit of large background noise and low reflectivity, there
is no need of symplectic diagonalization which usually complicates the
computation of decay constants. First, we show that two-mode squeezed vacuum
(TMSV) states are the optimal probe among pure Gaussian states with fixed
signal mean photon number. Second, as an alternative to preparing TMSV states
with high mean photon number, we show that preparing a TMSV state with low mean
photon number and displacing the signal mode is a more experimentally feasible
setup without degrading the performance that much. Third, we show that it is of
utmost importance to prepare an efficient idler memory to beat coherent states
and provide analytic bounds on the idler memory transmittivity in terms of
signal power, background noise, and idler memory noise. Finally, we identify
the region of physically possible correlations between the signal and idler
modes that can beat coherent states.Comment: 16 pages, 6 figure
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