Skew hook Schur functions and the cyclic sieving phenomenon

Fix an integer $t \geq 2$ and a primitive $t^{\text{th}}$ root of unity $\omega$. We consider the specialized skew hook Schur polynomial $\text{hs}_{\lambda/\mu}(X,\omega X,\dots,\omega^{t-1}X/Y,\omega Y,\dots,\omega^{t-1}Y)$, where $\omega^k X=(\omega^k x_1, \dots, \omega^k x_n)$, $\omega^k Y=(\omega^k y_1, \dots, \omega^k y_m)$ for $0 \leq k \leq t-1$. We characterize the skew shapes $\lambda/\mu$ for which the polynomial vanishes and prove that the nonzero polynomial factorizes into smaller skew hook Schur polynomials. Then we give a combinatorial interpretation of $\text{hs}_{\lambda/\mu}(1,\omega^d,\dots,\omega^{d(tn-1)}/1,\omega^d,\dots,\omega^{d(tm-1)})$, for all divisors $d$ of $t$, in terms of ribbon supertableaux. Lastly, we use the combinatorial interpretation to prove the cyclic sieving phenomenon on the set of semistandard supertableaux of shape $\lambda/\mu$ for odd $t$. Using a similar proof strategy, we give a complete generalization of a result of Lee--Oh (arXiv: 2112.12394, 2021) for the cyclic sieving phenomenon on the set of skew SSYT conjectured by Alexandersson--Pfannerer--Rubey--Uhlin (Forum Math. Sigma, 2021).Comment: 13 pages, 2 figure

Matching Latent Encoding for Audio-Text based Keyword Spotting

Using audio and text embeddings jointly for Keyword Spotting (KWS) has shown high-quality results, but the key challenge of how to semantically align two embeddings for multi-word keywords of different sequence lengths remains largely unsolved. In this paper, we propose an audio-text-based end-to-end model architecture for flexible keyword spotting (KWS), which builds upon learned audio and text embeddings. Our architecture uses a novel dynamic programming-based algorithm, Dynamic Sequence Partitioning (DSP), to optimally partition the audio sequence into the same length as the word-based text sequence using the monotonic alignment of spoken content. Our proposed model consists of an encoder block to get audio and text embeddings, a projector block to project individual embeddings to a common latent space, and an audio-text aligner containing a novel DSP algorithm, which aligns the audio and text embeddings to determine if the spoken content is the same as the text. Experimental results show that our DSP is more effective than other partitioning schemes, and the proposed architecture outperformed the state-of-the-art results on the public dataset in terms of Area Under the ROC Curve (AUC) and Equal-Error-Rate (EER) by 14.4 % and 28.9%, respectively

Flexible Keyword Spotting based on Homogeneous Audio-Text Embedding

Spotting user-defined/flexible keywords represented in text frequently uses an expensive text encoder for joint analysis with an audio encoder in an embedding space, which can suffer from heterogeneous modality representation (i.e., large mismatch) and increased complexity. In this work, we propose a novel architecture to efficiently detect arbitrary keywords based on an audio-compliant text encoder which inherently has homogeneous representation with audio embedding, and it is also much smaller than a compatible text encoder. Our text encoder converts the text to phonemes using a grapheme-to-phoneme (G2P) model, and then to an embedding using representative phoneme vectors, extracted from the paired audio encoder on rich speech datasets. We further augment our method with confusable keyword generation to develop an audio-text embedding verifier with strong discriminative power. Experimental results show that our scheme outperforms the state-of-the-art results on Libriphrase hard dataset, increasing Area Under the ROC Curve (AUC) metric from 84.21% to 92.7% and reducing Equal-Error-Rate (EER) metric from 23.36% to 14.4%

Improving vision-inspired keyword spotting using dynamic module skipping in streaming conformer encoder

Using a vision-inspired keyword spotting framework, we propose an architecture with input-dependent dynamic depth capable of processing streaming audio. Specifically, we extend a conformer encoder with trainable binary gates that allow us to dynamically skip network modules according to the input audio. Our approach improves detection and localization accuracy on continuous speech using Librispeech top-1000 most frequent words while maintaining a small memory footprint. The inclusion of gates also reduces the average amount of processing without affecting the overall performance. These benefits are shown to be even more pronounced using the Google speech commands dataset placed over background noise where up to 97% of the processing is skipped on non-speech inputs, therefore making our method particularly interesting for an always-on keyword spotter

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Search for light bosons in decays of the 125 GeV Higgs boson in proton-proton collisions at root s=8 TeV

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Search for supersymmetry in events with photons and missing transverse energy in pp collisions at 13 TeV

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Search for heavy gauge W ' bosons in events with an energetic lepton and large missing transverse momentum at root s=13TeV

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Search for single production of vector-like quarks decaying into a b quark and a W boson in proton-proton collisions at root s=13 TeV

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Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

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