Ressources

The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation when the "innovations" satisfy some "light" averaging properties in the presence of a pathwise Lyapunov function. These averaging assumptions allow us to unify apparently remote frameworks where the innovations are simulated (possibly deterministic like in Quasi-Monte Carlo simulation) or exogenous (like market data) with ergodic properties. We propose several fields of applications and illustrate our results on five examples mainly motivated by Finance.

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are fulfilled (using notably the co-monotony principle). We illustrate our results with numerical experiments on both simulated data and using a financial market dataset.

The goal of this paper is to critically evaluate a heuristic algorithm for the Inverse Banzhaf Index problem by Laruelle and Widgr\'en. Few qualitative results are known about the approximation quality of the heuristics for this problem. The intuition behind the operation of this approximation algorithm is analysed and evaluated. We found that the algorithm can not handle general inputs well, and often fails to improve inputs. It is also shown to diverge after only tens of iterations. We present three alternative extensions of the algorithm that do not alter the complexity but can result in up to a factor 6.5 improvement in solution quality.

This paper extends the link between stochastic approximation (SA) theory and randomized urn models developed in Laruelle, Pag{\`e}s (2013), and their applications to clinical trials introduced in Bai, HU (1999,2005) and Bai, Hu, Shen (2002). We no longer assume that the drawing rule is uniform among the balls of the urn (which contains d colors), but can be reinforced by a function f. This is a way to model risk aversion. Firstly, by considering that f is concave or convex and by reformulating the dynamics of the urn composition as an SA algorithm with remainder, we derive the a.s. convergence and the asymptotic normality (Central Limit Theorem, CLT) of the normalized procedure by calling upon the so-called ODE and SDE methods. An in-depth analysis of the case d=2 exhibits two different behaviors: A single equilibrium point when f is concave, and when f is convex, a transition phase from a single attracting equilibrium to a system with two attracting and one repulsive equilibrium points. The last setting is solved using results on non-convergence toward noisy and noiseless "traps" in order to deduce the a.s. convergence toward one of the attracting points. Secondly, the special case of a Polya urn (when the addition rule is the identity matrix) is analyzed, still using result from SA theory about "traps". Finally, these results are applied to a function with regular variation and to an optimal asset allocation in Finance.

Stochastic approximation algorithms have been the subject of an enormous body of literature, both theoretical and applied. Recently, Laruelle and Pag\`es (2013) presented a link between the stochastic approximation and response-adaptive designs in clinical trials based on randomized urn models investigated in Bai and Hu (1999, 2005), and derived the asymptotic normality or central limit theorem for the normalized procedure using a central limit theorem for the stochastic approximation algorithm. However, the classical central limit theorem for the stochastic approximation algorithm does not include all cases of its regression function, creating a gap between the results of Laruelle and Pag\`es (2013) and those of Bai and Hu (2005) for randomized urn models. In this paper, we establish new central limit theorems of the stochastic approximation algorithm under the popular Lindeberg condition to fill this gap. Moreover, we prove that the process of the algorithms can be approximated by a Gaussian process that is a solution of a stochastic differential equation. In our application, we investigate a more involved family of urn models and related adaptive designs in which it is possible to remove the balls from the urn, and the expectation of the total number of balls updated at each stage is not necessary a constant. The asymptotic properties are derived under much less stringent assumptions than those in Bai and Hu (1999, 2005) and Laruelle and Pag\`es (2013).

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues.

This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated in Bai and Hu (1999,2005) and Bai, Hu and Shen (2002). We reformulate the dynamics of both the urn composition and the assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the a.s. convergence and the asymptotic normality (CLT) of the normalized procedure under less stringent assumptions by calling upon the ODE and SDE methods. As a second step, we investigate a more involved family of models, known as multi-arm clinical trials, where the urn updating depends on the past performances of the treatments. By increasing the dimension of the state vector, our SA approach provides this time a new asymptotic normality result.

We report on non-linear magneto-tunneling experiments carried out in single GaAs vertical quantum dots. We show that conduction at low voltage bias can be a spectroscopic tool for both the ground state and first excited states of few electrons on the dot. Increasing voltage a large resonant peak is observed and attributed to tunneling across the quasi-continuum of higher excited states.

A Fano resonance mechanism is evidenced to control the formation of optical Fermi-edge singularities in multi-subband systems such as remotely doped AlxGa1-xAs heterostructures. Using Fano parameters, we probe the physical nature of the interaction between Fermi-sea electrons and empty conduction subbands. We show that processes of extrinsic origin like alloy-disorder prevail easily at 2D over multiple diffusions from charged valence holes expected by many-body scenarios.

In this paper, we consider coordination and anti-coordination heterogeneous games played by a finite population formed by different types of individuals who fail to recognize their own type but do observe the type of their opponent. We show that there exists symmetric Nash equilibria in which players discriminate by acting differently according to the type of opponent that they face in anti-coordination games, while no such equilibrium exists in coordination games. Moreover, discrimination has a limit: the maximum number of groups where the treatment differs is three. We then discuss the theoretical results in light of the observed behavior of people in some specific psychological contexts.

<p>With Principles of Non-Philosophy, Laruelle elaborates on the concepts and methods of non-philosophy with even greater attention. Yet he carries out this elaboration without much mention or textual analysis of the history of philosophy one sees in Philosophies of Difference. This is in part because Principles of Non-Philosophy aims to elaborate the very project it is detailing without any distance between that elaboration and the project itself. It is wildly constructivist and undeniably rooted in the history of the European philosophical tradition.</p>

<p>Article is devoted to ethical aspect of a performativity which usually remains beyond the scope of esthetic, political, linguistic aspects. In modern performance studies are usually combined the private and exact entered by Ostin definition of a performativity as the word making action, and widespread Marxist idea of the critical, changing the world theory potential. In article the main rate becomes on the heterodox reading of a performativity following criticism of violence of metaphysics of Levinas. If the theory is output from ethics, then the performativityt is thought as radical passivity of the theory. In that case, crucial importance for conceptual model of the subject is gained by not epistemological, but ethical measurement, namely ethics of a categorical imperative. The categorical imperative is arranged as a performatory contradiction between desire and a will, it fixes a situation of a gap, an akrasia, otherwise, of the decision. Two modern interpretations of value of a concept of the subject of the decision are given in article. One of them - positive, belongs Badiou, it is the subject of fidelity to an event. It will be coordinated with the subject of practical mind of Kant as it is supported by the pure and formal movement of will. However this model, according to Meillassoux, can be considered transitional as the exclusivity of the decision undermines a correlation circle. The criticism of the Philosophical Decision as distributions of transcendental and empirical functions, offered by Laruelle appears really fresh course. Non-philosophy thinks of itself as the only performatory theory because it registers this initial decision and refuses to go on a speculative circular way of philosophizing. The main problem connected with non - philosophy, consists that its performativity remains rather declarative, conditions of a solution of the problem of an akrasia, a gap between desirable and possible are not clear.</p> <p>&nbsp;</p>

<p>SET and examples shown in the paper &#39;Unraveling spatial cellular pattern by computational tissue shuffling&#39; (E. Laruelle, N. Spassky, A.Genovesio)</p>

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<p>In <em>Elden Ring</em>, the Shabriri Grape serves as a focal point for the metaphysical speculation that has become distinctive of the studio's oeuvre under the tenure of game director and now company president Hidetaka Miyazaki. As the player-character blindly pulls on the threads of Queen Marika's Golden Order, woven as they are throughout the Lands Between, they find themselves inducted into a metaphysical investigation. <em>Elden Ring</em> toys with questions of ontology and subjectivity that challenge the idealist branch of the Western philosophical canon, and in so doing introduces a ludic torsion that requires its players to come to terms with notions of the real and its organization that go back to the beginning of recorded critical inquiry. <em>Elden Ring</em>, redoubling the stylistics of its forebears, is distinctly hermetic in its narrative construction, and consequently it requires of its players a hermeneutic sensibility, a willingness to engage in the interpretation of the textual traces scattered throughout its gameworld, traces such as those which accompany the Shabriri Grape. To follow the guidance of this "yellowing, oozing eyeball," to set off in pursuit of the "distant light" it reveals, the player-character must go to the limits of their knowledge, indeed to the very limit of knowledge as such, to the original scission or abyss from which the world of <em>Elden Ring</em> was born.</p>

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<p>Through the philosophies of Martin Heidegger, Jacques Derrida, and Fran&ccedil;ois Laruelle, this paper deconstructs the metaphysics of the sun that undergirds the worlds of the three <em>Dark Souls </em>games developed by FromSoftware, while also identifying the internal critique of this metaphysics that the <em>Dark Souls </em>games successively elaborate. Indeed, as inversions of the western fantasy model, the three <em>Dark Souls </em>games also labour to invert western <em>philosophy</em>, striking at the heart of Platonic idealism and its variations throughout history.</p>

<div>This article explores how forming a collective Central Asian identity can serve</div> <div>as a foundation for meaningful regional integration. While geopolitical challenges and the legacy</div> <div>of Soviet rule have long hindered cooperation among the five republics, recent developments&mdash;</div> <div>particularly Uzbekistan&rsquo;s shift toward regionalism since 2016&mdash;have renewed attention on</div> <div>shared cultural and historical ties. The paper argues that a common identity is not merely</div> <div>symbolic, but a practical step toward stronger political, economic, and social bonds. Drawing on</div> <div>constructivist and postcolonial approaches, it examines the opportunities and obstacles involved</div> <div>in building this identity, including nationalist narratives, external influence, and historical</div> <div>divisions. Ultimately, the article suggests that a shared regional identity could help Central Asian</div> <div>states strengthen internal unity, manage cross-border issues more effectively, and assert greater</div> <div>autonomy in the global arena.</div>

<p>This paper proposes a systematic reconstruction of philosophical theory construction. It argues that the essence of philosophy does not lie in describing reality but in formally generating the conditions under which reality becomes intelligible. Philosophical theory construction is defined as the act of assigning to any conceptual or empirical content an abstract, theory-internal form endowed with meaning specific to that theoretical context. This process constitutes an interface between philosophy and non-philosophy: within philosophy, the form creates meaning; beyond philosophy, it provides a structure through which the empirical world can be interpreted. The paper develops a four-layer model&mdash;formal attribution, theory-internal meaning, interface mediation, and formal narrative reasoning&mdash;and situates it within the history of philosophical thought from Kant to Badiou. It concludes that philosophy&rsquo;s originality resides in its capacity to construct formal truth rather than empirical truth, thereby offering a model for future interdisciplinary and computational applications of philosophical method.</p>

<p>&nbsp;In April 2022, we have run a voting experiment during the French presidential election. During this experiment, participants were asked to test several alternative voting methods to elect the French president, like scoring methods, instant-runoff voting, Borda&nbsp;with partial rankings, majority judgement and pairwise comparisons. The experiment was both carried out <em>in situ </em>in polling stations during the first round of the presidential election (using paper ballots), and online between April 8th (two days before the first round of the election) and May 7th (using a web application). A total of 2308 participants took part in the online experiment. This dataset contains the answers provided by the participants to the online experiment, with no other processsing than a basic transformation to a set of CSV files.</p> <p>The companion paper available on this repository describes the experimental protocol, the format of the files, and summarizes the precise conditions under which this dataset is available.</p>