Greedy algorithms for high-dimensional non-symmetric linear problems

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor product functions, each term of which is iteratively computed via a greedy algorithm. There exists a good theoretical framework for these methods in the case of (linear and nonlinear) symmetric elliptic problems. However, the convergence results are not valid any more as soon as the problems considered are not symmetric. We present here a review of the main algorithms proposed in the literature to circumvent this difficulty, together with some new approaches. The theoretical convergence results and the practical implementation of these algorithms are discussed. Their behaviors are illustrated through some numerical examples.Comment: 57 pages, 9 figure

Convergence of a greedy algorithm for high-dimensional convex nonlinear problems

In this article, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided that the gradient of the energy is Lipschitz on bounded sets. The main interest of this method is that it can be used for high-dimensional nonlinear convex problems. We illustrate this method on a prototypical example for uncertainty propagation on the obstacle problem.Comment: 36 pages, 9 figures, accepted in Mathematical Models and Methods for Applied Science

An embedded corrector problem to approximate the homogenized coefficients of an elliptic equation

We consider a diffusion equation with highly oscillatory coefficients that admits a homogenized limit. As an alternative to standard corrector problems, we introduce here an embedded corrector problem, written as a diffusion equation in the whole space in which the diffusion matrix is uniform outside some ball of radius $R$. Using that problem, we next introduce three approximations of the homogenized coefficients. These approximations, which are variants of the standard approximations obtained using truncated (supercell) corrector problems, are shown to converge when $R \to \infty$. We also discuss efficient numerical methods to solve the embedded corrector problem

Cosine-similarity penalty to discriminate sound classes in weakly-supervised sound event detection.

The design of new methods and models when only weakly-labeled data are available is of paramount importance in order to reduce the costs of manual annotation and the considerable human effort associated with it. In this work, we address Sound Event Detection in the case where a weakly annotated dataset is available for training. The weak annotations provide tags of audio events but do not provide temporal boundaries. The objective is twofold: 1) audio tagging, i.e. multi-label classification at recording level, 2) sound event detection, i.e. localization of the event boundaries within the recordings. This work focuses mainly on the second objective. We explore an approach inspired by Multiple Instance Learning, in which we train a convolutional recurrent neural network to give predictions at frame-level, using a custom loss function based on the weak labels and the statistics of the frame-based predictions. Since some sound classes cannot be distinguished with this approach, we improve the method by penalizing similarity between the predictions of the positive classes during training. On the test set used in the DCASE 2018 challenge, consisting of 288 recordings and 10 sound classes, the addition of a penalty resulted in a localization F-score of 34.75%, and brought 10% relative improvement compared to not using the penalty. Our best model achieved a 26.20% F-score on the DCASE-2018 official Eval subset close to the 10-system ensemble approach that ranked second in the challenge with a 29.9% F-score

Problematika Yuridis Putusan Mahkamah Konstitusi Nomor 20/PUU-XIV/2016 Terkait Alat Bukti Penyadapan

AbstrakMahkamah Konstitusi (MK) sebagai salah satu lembaga penegak hukum di Indonesia yang berperan dalam mendorong dan melakukan pembaharuan hukum, peradilan dan demokrasi. Kewenangan MK dalam pengujian Undang-undang terhadap Undang-Undang Dasar Negara Republik Indonesia 1945 sering kali menarik perhatian dan mempengaruhi berlakunya hukum di Indonesia. Pengujian Undang-Undang yang cukup menarik perhatian masyarakat yakni pada perkara Nomor : 20/PUU-XIV/2016 terkait alat bukti penyadapan. Pemohon dalam pengujian a quo adalah Setya Novanto yang merupakan Anggota DPR RI yang masih berstatus aktif. Dalam Permohonan tersebut pemohon mengajukan pengujian konstitusional Pasal 5 ayat (1) dan ayat (2) serta Pasal 44 huruf b Undang-Undang Nomor 11 Tahun 2008 tentang Informasi dan Transaksi Elektronik dan Pasal 26 A Undang-Undang Republik Indonesia Nomor 20 Tahun 2001 tentang Pemberantasan Tindak Pidana Korupsi terhadap Pasal 28 G ayat (1) Undang-Undang Dasar Negara Republik Indonesia Tahun 1945. Putusan tersebut bersifat Tidak Konstitusional Bersyarat (Conditionally Unconstitusional), di mana dari sembilan majelis 2 (dua) hakim konstitusi memiliki pendapat berbeda (Dissenting Opinions). Tujuan dari penelitian ini ialah menganalisis pertimbangan hakim dalam Putusan MK Nomor : 20/PUU-XIV/2016 dan akibat hukum penyadapan setelah adanya putusan tersebut terhadap peraturan perundang-undangan. Jenis penelitian yang digunakan dalam penulisan skripsi ini adalah yuridis normatif dengan pendekatan perundang-undangan, pendekatan kasus dan pendekatan konseptual. Berdasarkan hasil penelitian dapat disimpulkan bahwa Mahkamah menilai warga Negara Indonesia yang juga menyandang status sebagai anggota DPR-RI akan dipertimbangkan tersendiri terhadap kedudukan hukumnya sesuai dengan kerugian konstitusional yang didalilkan. Dalam pertimbangan selanjutnya mahkamah menilai kerugian konstitusional pemohon tersebut memiliki hubungan sebab akibat dengan berlakunya frasa informasi elektronik dan/atau dokumen elektronik. Akibat hukum Putusan Mahkamah Konsitusi adalah setiap orang yang melakukan penyadapan sebagai alat bukti dalam rangka penegakan hukum harus mengacu pada persyaratan yang ditetapkan oleh Putusan Mahkamah Konstitusi yaitu penyadapan harus dilakukan atas permintaan aparat penegak hukum yaitu Kepolisian, Kejaksaan dan/atau institusi penegak hukum lainnya. Saran yang dapat penulis sampaikan bahwa perlu adanya batasan kedudukan hukum anggota Dewan Perwakilan Rakyat dalam mengajukan permohonan pengujian konstitusional ke Mahkamah Konstitusi.   Kata Kunci: Putusan Mahkamah Konstitusi, Penyadapan, Kedudukan Hukum.AbstractThe Constitutional Court as one of the law enforcement agencies in Indonesia that plays a role in encouraging and reforming law, justice and democracy. The authority of the Constitutional Court in examining laws against the 1945 Constitution of the Republic of Indonesia often attracts attention and influences the entry into force of law in Indonesia. Testing of Law which is quite interesting to the public, namely in case Number: 20 / PUU-XIV / 2016 related to evidence of wiretapping. The applicant in the a quo test was Setya Novanto, who is a Member of the Indonesian Parliament who is still active. In the petition the petitioners submit constitutional review of Article 5 paragraph (1) and paragraph (2) as well as Article 44 letter b of Law Number 11 Year 2008 concerning Electronic Information and Transactions and Article 26 A Law of the Republic of Indonesia Number 20 of 2001 concerning Eradication Corruption Crime against Article 28 G paragraph (1) of the 1945 Constitution of the Republic of Indonesia. The verdict is Conditionally Unconstitutional, in which of the nine assemblies 2 (two) constitutional judges have different opinions (Dissenting Opinions). The purpose of this study is to analyze the judgment of judges in the Constitutional Court Decision Number: 20 / PUU-XIV / 2016 and the legal consequences of wiretapping after the verdict on the laws and regulations. This type of research used in writing this thesis is a normative juridical approach to legislation, case approaches and conceptual approaches. Based on the results of the study, it can be concluded that the Court considers that Indonesian citizens who also hold the status as members of the House of Representative of Indonesia Republic will be considered separately for their legal position in accordance with the postulated constitutional impairment. In further consideration the court considered the applicant's constitutional impairment to have a causal relationship with the enactment of the electronic information phrase and / or electronic document. The legal consequences of the Constitutional Court Decision is that every person who conducts wiretapping as evidence in the context of law enforcement must refer to the requirements stipulated by the Constitutional Court Decision, namely wiretapping must be done at the request of law enforcement officials namely the Police, Prosecutors' Office and / or other law enforcement institutions. Suggestions that the author can convey that it is necessary to limit the legal standing of members of the House of Representatives in submitting an application for constitutional testing to the Constitutional Court.   Keywords: Constitutional Court Decision, Wiretapping, Legal Standing

Des innovations institutionnelles pour diminuer l'utilisation de pesticides en bananeraie et protéger la ressource eau

Depuis plusieurs décennies, la canne et la banane, monocultures fortement dépendantes des intrants, façonnent le paysage guadeloupéen de manière binaire : canne au Nord et banane au Sud1. Introduite en Guadeloupe au XVIIe siècle, la banane n’a commencé à être exportée qu’au début du XXe siècle, avec le développement des traitements phytosanitaires et l’apport d’engrais : la production connaît alors un essor important, au détriment des cultures vivrières et de la canne à sucre

Error Probability Bound Considering Beat Noise in 2-D OCDMA Systems

Considering a 2-Dimensional Optical Code Division Multiple Access (2-D OCDMA) system using spreading codes in both time and wavelength domains, we study in this paper the impact on the performance of one of the most predominant performance limitation which is beat noise due to the photo detection. The beat noise impact is correlated with the wellknown OCDMA limitation named Multiple Access Interference (MAI). Our contribution is to assess, through a theoretical analysis, an error probability bound of a system working in incoherent or partially coherent optical regime. Thanks to the theoretical error probability expression we have developed, the specifications and requirements needed to neglect beat noise effect in a 2-D OCDMA system with a conventional receiver are easily obtained. For a targeted Bit Error Rate (BER), and a given number of active users, one can determine from our results, the 2-D code family parameters, the available data rate and the optical source characteristics, required to be free of beat noise impact