The Emergence of Law Consultants

In this paper we study a slightly subcritical Choquard problem on a bounded domain A. We prove that the number of positive solutions depends on the topology of the domain. In particular when the exponent of the nonlinearity approaches the critical one, we show the existence of cat (A) + 1 solutions. Here cat (A) denotes the Lusternik–Schnirelmann category

Better Word Embeddings by Disentangling Contextual n-Gram Information

Pre-trained word vectors are ubiquitous in Natural Language Processing applications. In this paper, we show how training word embeddings jointly with bigram and even trigram embeddings, results in improved unigram embeddings. We claim that training word embeddings along with higher n-gram embeddings helps in the removal of the contextual information from the unigrams, resulting in better stand-alone word embeddings. We empirically show the validity of our hypothesis by outperforming other competing word representation models by a significant margin on a wide variety of tasks. We make our models publicly available.Comment: NAACL 201

Unsupervised Learning of Sentence Embeddings using Compositional n-Gram Features

The recent tremendous success of unsupervised word embeddings in a multitude of applications raises the obvious question if similar methods could be derived to improve embeddings (i.e. semantic representations) of word sequences as well. We present a simple but efficient unsupervised objective to train distributed representations of sentences. Our method outperforms the state-of-the-art unsupervised models on most benchmark tasks, highlighting the robustness of the produced general-purpose sentence embeddings.Comment: NAACL 201

Geometry and life of urban space

This essay introduces rules for building new urban squares, and for fixing existing ones that are dead. The public square as a fundamental urban element behaves both as a node and as a connector of the urban fabric. Like the components of an organism, each urban element is itself highly complex, and this conception contradicts postwar design trends based on abstract simplistic ideas: those are imposed in order to control instead of stimulating social life. Urban structures, infrastructure, human beings, their activity nodes, and all their interconnections come together to form a “super-organism”, a complex and dynamic whole that is the city. This happens only when the geometry of the urban fabric is encouraged to develop in a living manner. The basic element of this “super-organism” is urban space that works with informational processes. In European culture, the square connects the local urban space with other squares, streets, and roads with a strong pedestrian use. A living city works through its connections to reach the properties of a “super-organism”

DoGE: Domain Reweighting with Generalization Estimation

The coverage and composition of the pretraining data corpus significantly impacts the generalization ability of large language models. Conventionally, the pretraining corpus is composed of various source domains (e.g. CommonCrawl, Wikipedia, Github etc.) according to certain sampling probabilities (domain weights). However, current methods lack a principled way to optimize domain weights for ultimate goal for generalization. We propose DOmain reweighting with Generalization Estimation (DoGE), where we reweigh the sampling probability from each domain based on its contribution to the final generalization objective assessed by a gradient-based generalization estimation function. First, we train a small-scale proxy model with a min-max optimization to obtain the reweighted domain weights. At each step, the domain weights are updated to maximize the overall generalization gain by mirror descent. Finally we use the obtained domain weights to train a larger scale full-size language model. On SlimPajama-6B dataset, with universal generalization objective, DoGE achieves better average perplexity and zero-shot reasoning accuracy. On out-of-domain generalization tasks, DoGE reduces perplexity on the target domain by a large margin. We further apply a parameter-selection scheme which improves the efficiency of generalization estimation

Verso il reale: schizofrenia/psicoanalisi

The paper aims to develop a path through Lacan’s teaching and writings upon the relationship between psychoanalysis and schizophrenia. Particularly, it wants to show the movement from Symbolic to Real, element present both in schizophrenia and in the psychoanalytic practice, although the highlighted structural divergence in this movement between two sides. The different articulations of subject between symbolic and real, living body and language/signifier, are here exposed through three paradigms inferred from Lacan’s teaching. Particular attention is devoted to the concept of pousse-à-la-femme (pushtowards- woman), introduced by Jacques Lacan through the figure of Schreber, as a paradigmatic condition of psychosis. In fact, this push is characterized by the movement towards Real and the exception of not-all and the feminine jouissance.The paper aims to develop a path through Lacan’s teaching and writings upon the relationship between psychoanalysis and schizophrenia. Particularly, it wants to show the movement from Symbolic to Real, element present both in schizophrenia and in the psychoanalytic practice, although the highlighted structural divergence in this movement between two sides. The different articulations of subject between symbolic and real, living body and language/signifier, are here exposed through three paradigms inferred from Lacan’s teaching. Particular attention is devoted to the concept of pousse-à-la-femme (pushtowards- woman), introduced by Jacques Lacan through the figure of Schreber, as a paradigmatic condition of psychosis. In fact, this push is characterized by the movement towards Real and the exception of not-all and the feminine jouissance

Fractional minimal surfaces and Allen-Cahn equations

In recent years fractional operators have received considerable attention both in pure and applied mathematics. They appear in biological observations, finance, crystal dislocation, digital image reconstruction and minimal surfaces. In this thesis we study nonlocal minimal surfaces which are boundaries of sets minimizing certain integral norms and can be interpreted as a non-infinitesimal version of classical minimal surfaces. In particular, we consider critical points, with or withouth constraints, of suitable functionals, or approximations through diffuse models as the Allen-Cahn\u2019s. In the first part of the thesis we prove an existence and multiplicity result for critical points of the fractional analogue of the Allen-Cahn equation in bounded domains. We bound the functional using a standard nonlocal tool: we split the domain in two regions and we analyze the three significative interactions. Then, the proof becomes an application of a classical Krasnoselskii\u2019s genus result. Then, we consider a fractional mesoscopic model of phase transition i.e. the fractional Allen-Cahn equation with the addition of a mesoscopic term changing the \u2018pure phases\u2019 \ub11 in periodic functions. We investigate geometric properties of the interface of the associated minimal solutions. Then we construct minimal interfaces lying to a strip of prescribed direction and universal width. We provide a geometric and variational technique adapted to deal with nonlocal interactions. In the last part of the thesis, we study functionals involving the fractional perimeter. In particular, first we study the localization of sets with constant nonlocal mean curvature and small prescribed volume in an open bounded domain, proving that these sets are \u2018sufficiently close\u2019 to critical points of a suitable potential. The proof is an application of the Lyupanov-Schmidt reduction to the fractional perimeter. Finally, we consider the fractional perimeter in a half-space. We prove the existence of a minimal set with fixed volume and some of its properties as intersection with the hyperplane {xN = 0}, symmetry, to be a graph in the xN-direction and smoothness