Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility

We consider Galerkin approximations of eigenvalue problems for holomorphic Fredholm operator functions for which the operators do not have the structure “coercive+compact”. In this case the regularity (in the vocabulary of discrete approximation schemes) of Galerkin approximations is not unconditionally satisfied and the question of convergence is delicate. We report a technique to prove regularity of approximations which is applicable to a wide range of eigenvalue problems. The technique is based on the knowledge of a suitable Test function operator. In particular, we introduce the concepts of weak T-coercivity and T-compatibility and prove that for weakly T-coercive operators, T-compatibility of Galerkin approximations implies their regularity. Our framework can be successfully applied to analyze e.g. complex scaling/perfectly matched layer methods, problems involving sign-changing coefficients due to meta-materials and also (boundary element) approximations of Maxwell-type equations. We demonstrate the application of our framework to the Maxwell eigenvalue problem for a conductive material.

Reposisi BULOG dalam Rencana Pembentukan Badan Pangan Nasional (Repositioning of BULOG in The Formation Plan of National Food Agency )

ABSTRAK Selama ini peran regulator pangan di Indonesia dijalankan oleh beberapa Kementerian yang berbeda-beda, akibatnya kebijakan pangan menjadi terpilah-pilah di beberapa Kementerian/Lembaga (K/L), dan sering tumpang tindih, sehingga Perum BULOG selaku operator pangan harus berkoordinasi dan bertanggung jawab kepada banyak K/L. Kondisi tersebut menyebabkan berbagai kendala dalam pelaksanaan penugasan, baik dari sisi operasional maupun sisi finansial. Tulisan ini bertujuan untuk : (i) memberikan gambaran terkait penugasan, peran dan kendala yang dihadapi BULOG sebagai lembaga pangan yang diamanatkan Pemerintah dalam menjaga ketahanan pangan khususnya pada komoditas beras; (ii) mereviu model kelembagaan pangan di negara lain ; dan (iii) Menganalisis berbagai skenario atas reposisi peran dan fungsi Perum BULOG dalam rencana pembentukan Badan Pangan Nasional di masa mendatang. Pemerintah menugaskan Perum BULOG dalam menjaga ketersediaan pangan dan stabilisasi harga pangan di tingkat konsumen dan produsen pada beberapa pangan pokok. Kendala yang dihadapi BULOG dalam pelaksanaan penugasan, baik dari segi operasional maupun finansial, yaitu: Pertama, BULOG harus mengeluarkan banyak energi, waktu dan koordinasi yang intensif dan melakukan pengendalian sepanjang rantai nilai. Kedua, BULOG kesulitan dalam perencanaan dan pelaksanaan karena efektivitas stabilisasi pangan mensyaratkan pemanfaatan alur distribusi yang mapan. Ketiga, penugasan penyerapan dan penyediaan stok kebutuhan pangan tidak didukung pendanaan dari pemerintah. Hal tersebut akan mempersulit BULOG, karena BULOG harus menanggung beban atas beras PSO yang dikelolanya. Dalam rencana pembentukan BPN, pembelajaran kunci terhadap lembaga pangan di negara lain seperti Cina, India, Filipina, Malaysia, Thailand, Vietnam, Norwegia, dan Denmark yaitu terdapat pemisahan yang jelas antara regulator dan operator dalam pelaksana bidang pangan. Regulator pangan bertanggung jawab langsung ke Presiden dan operator pangan bertanggung jawab langsung pada satu lembaga independen atau kementerian yang berada di bawah presiden dan memberikan masukan secara aktif kepada regulator. Dalam kaitan dengan itu, ada tiga opsi model pembentukan Badan Pangan Nasional (BPN): Pertama, BULOG ditransformasikan menjadi BPN. Pada opsi pertama tidak terdapat pemisahan antara regulator dan operator, dan lembaga operator hanya dapat melakukan penugasan PSO, tidak termasuk bisnis komersial. Sebagai konsekuensinya pemerintah harus menyediakan anggaran yang relatif lebih besar untuk keperluan biaya penugasan dan operasional lembaga. Kedua, transformasi BPN dari organ kementerian sedangkan BULOG tetap sebagai BUMN. Kelembagaan BULOG sebagai BUMN operator pangan tidak berubah. Ketiga, BULOG sebagai operator di bawah BPN, dengan pemisahan yang jelas antara fungsi regulator dan operator. Fungsi kelembagaan BULOG sebagai BUMN di bawah kendali BPN akan lebih diperkuat sehingga lebih mendukung upaya pencapaian target penugasan yang diberikan oleh BPN. kata kunci : BULOG, Operator, Regulator, ketahanan pangan, Badan Pangan Nasional ABSTRACT The food regulator's role in Indonesia has been carried out by several different Ministries so far. As a result, food policies have has become fragmented in several Ministries/ Agencies. It often overlaps, so that Perum BULOG, as the food operator, must coordinate and be responsible to many Ministers/agencies. This condition causes all problems and various obstacles in implementing assignments both on operational and financial sides. This paper aims to: (i) Provide an overview of the assignments, roles, and constraints faced by BULOG as a food institution mandated by the Government in maintaining food security, especially in rice commodities; (ii) Review different models of food institutions in other countries; (iii) Analyze various scenarios for repositioning the roles and functions of Perum BULOG in the formation plan of the National Food Agency in the future. The Government has assigned Perum BULOG to maintain food availability and stabilize several staple food prices both at the consumer and producer levels. Several obstacles faced by BULOG in implementing assignments both on operational and financial sides, including first, BULOG must spend a lot of time, energy, and intensive coordination and control along the value chain. Second, BULOG has difficulties in planning and implementation due to the effectiveness of food stabilization requires the use of an established distribution channels. Third, the assignment of the required food procurement and distribution is not supported by government funding. These problems have created difficulties for BULOG since BULOG has to bear the financial consequences of public service obligation costs it manages. In the formation plan of BPN, a key lesson for food institutions in other countries such as China, India, Philippines, Malaysia, Thailand, Vietnam, Norway, and Denmark is that there is a clear separation between regulators and operators in implementing the food sector. Food regulators are directly responsible to the President and food operators are directly responsible to an independent agency or ministry under the President and provide active inputs to regulators. In this regard, there are three model options for the formation of the National Food Agency (BPN). First, BULOG is transformed into BPN. In this option, there is no separation between the regulator and the operator, and the operator agency can only carry out PSO assignments, but not including commercial business. Consequently, the Government must provide a relatively larger budget for the institution's assignment and operational costs. Second, the transformation of the BPN from the ministry's organs while BULOG remains as a State Owned Enterprise. BULOG's institution as a state-owned food operator has not changed. Third, BULOG as an operator under BPN, with a clear separation between regulator and operator functions. The institutional role of BULOG as a State Owned Enterpirse under the control of BPN will be further strengthened to support further efforts to achieve the assignment targets given by BPN. keywords: BULOG, Operators, Regulators, food security, National Food Agency

A Smoothed LASSO Based DNN Sparsification Technique

<div>Deep Neural Networks (DNNs) are increasingly being used in a variety of applications. However, DNNs have huge computational and memory requirements. One way to reduce these requirements is to sparsify DNNs by using smoothed LASSO (Least Absolute Shrinkage and Selection Operator) functions. In this paper, we show that for the same maximum error with respect to the LASSO function, the sparsity values obtained using various smoothed LASSO functions are similar. We also propose a layer-wise DNN pruning algorithm, where the layers are pruned based on their individual allocated accuracy loss budget determined by estimates of the reduction in number of multiply-accumulate operations (in convolutional layers) and weights (in fully connected layers). Further, the structured LASSO variants in both convolutional and fully connected layers are explored within the smoothed LASSO framework and the tradeoffs involved are discussed. The efficacy of proposed algorithm in enhancing the sparsity within the allowed degradation in DNN accuracy and results obtained on structured LASSO variants are shown on MNIST, SVHN, CIFAR-10, and Imagenette datasets.</div>

A Smoothed LASSO Based DNN Sparsification Technique

<div>Deep Neural Networks (DNNs) are increasingly being used in a variety of applications. However, DNNs have huge computational and memory requirements. One way to reduce these requirements is to sparsify DNNs by using smoothed LASSO (Least Absolute Shrinkage and Selection Operator) functions. In this paper, we show that for the same maximum error with respect to the LASSO function, the sparsity values obtained using various smoothed LASSO functions are similar. We also propose a layer-wise DNN pruning algorithm, where the layers are pruned based on their individual allocated accuracy loss budget determined by estimates of the reduction in number of multiply-accumulate operations (in convolutional layers) and weights (in fully connected layers). Further, the structured LASSO variants in both convolutional and fully connected layers are explored within the smoothed LASSO framework and the tradeoffs involved are discussed. The efficacy of proposed algorithm in enhancing the sparsity within the allowed degradation in DNN accuracy and results obtained on structured LASSO variants are shown on MNIST, SVHN, CIFAR-10, and Imagenette datasets.</div>

A Smoothed LASSO Based DNN Sparsification Technique

<div>Deep Neural Networks (DNNs) are increasingly being used in a variety of applications. However, DNNs have huge computational and memory requirements. One way to reduce these requirements is to sparsify DNNs by using smoothed LASSO (Least Absolute Shrinkage and Selection Operator) functions. In this paper, we show that for the same maximum error with respect to the LASSO function, the sparsity values obtained using various smoothed LASSO functions are similar. We also propose a layer-wise DNN pruning algorithm, where the layers are pruned based on their individual allocated accuracy loss budget determined by estimates of the reduction in number of multiply-accumulate operations (in convolutional layers) and weights (in fully connected layers). Further, the structured LASSO variants in both convolutional and fully connected layers are explored within the smoothed LASSO framework and the tradeoffs involved are discussed. The efficacy of proposed algorithm in enhancing the sparsity within the allowed degradation in DNN accuracy and results obtained on structured LASSO variants are shown on MNIST, SVHN, CIFAR-10, and Imagenette datasets.</div>