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A holographic uniqueness theorem for the two-dimensional Helmholtz equation
No full textInternational audienceWe consider a plane wave, a radiation solution, and the sum of thesesolutions (total solution) for the Helmholtz equation in an exterior region in .We consider a straight line in this region, such that the direction of propagation of the plane wave is not parallel to this line.We show that the radiation solution in the exterior region is uniquely determined by the intensity of the total solution on an interval of this line.In particular, this result solves one of the old mathematical questions of holography in its two-dimensional setting. Our proofs also contribute to the theory of the Karp expansion of radiation solutions in two dimensions
Test of lepton flavor universality in semileptonic B meson decays in proton-proton collisions at = 13 TeV
No full textInternational audienceA measurement of the ratio of branching fractions (J/) = (B J/)/(B J/) in the J/, decay channel is presented. This measurement uses a sample of proton-proton collision data collected at a center-of-mass energy of 13 TeV by the CMS experiment in 2018, corresponding to an integrated luminosity of 59.7 fb. The measured ratio, (J/) = 0.17 (stat) (syst) (theo) = 0.17 0.33, agrees with the value of 0.2582 0.0038 predicted by the standard model, which assumes lepton flavor universality
Twist corrections to exclusive vector meson production in a saturation framework
No full textInternational audienceWe develop a framework combining the higher-twist formalism of exclusive processes in the channel with the semi-classical effective description of small- physics in the channel. We apply it to transversely polarized light vector meson production, , which starts at the next-to-leading power and for which a purely collinear treatment leads to end-point singularities. The result is obtained in the most general kinematics, including both forward and non-forward cases by preserving the full impact parameter dependence in the non-perturbative correlators, in both momentum and coordinate space representations. A systematic expansion of the Wilson lines in terms of Reggeized gluon fields is performed in order to obtain the results in the weak-field BFKL approximation. These new results will allow for investigating the dilute-to-dense regime transition of QCD for a wide class of observables
"Mark Twain, un admirateur inattendu", chapitre d'ouvrage, sous la direction d'Aurélie Barjonet et Timo Kehren
No full textInternational audienceSamuel Langhorne Clemens, de son nom de plume Mark Twain, a permis à la littérature étatsunienne de se détacher de la littérature britannique, de sa langue et de ses normes grâce à toute cette oralité qui caractérise son célèbre roman "The Adventures of Huckleberry Finn" (1884). Selon Pascale Casanova, avec ce roman « le monde littéraire et le public américains pouvaient revendiquer une véritable “américanité”, une oralité, une spécificité, donc une différence reposant sur toutes les variantes dialectales du melting pot». Si Twain rompt avec la littérature anglaise, il convient de se demander quel rôle a pu jouer, dans son œuvre, la littérature produite dans la capitale de cette république mondiale des lettres décrite par Casanova. Force est de constater que Twain eut un vif intérêt pour le naturalisme d’Émile Zola. Afin de découvrir quel rôle Zola a pu jouer en filigrane pour Twain – qu’Hemingway identifie lui aussi comme le père fondateur d’une littérature nationale – cette étude propose une exploration de la dimension matérielle de la réception de Zola par Twain. L’analyse s’appuiera sur les séjours de Twain en France, ses amitiés réelles et virtuelles (via sa collection de cartes de visite), ses lectures des textes zoliens ainsi que ses écrits sur – et symboliquement aux côtés de – Zola. Mon hypothèse est que la recherche de la vérité et ce que Sydney J. Krause nomme « l’oppositionnisme » de Twain rencontrent la posture de Zola, à la fois en tant qu’écrivain et intellectuel, notamment dans un essai que Twain consacre au roman "La Terre" (1887) et dans ses notes griffonnées dans un exemplaire de "Rome" de 1896
Efficiency of neural quantum states in light of the quantum geometric tensor
No full textInternational audienceNeural quantum state (NQS) ans\"atze have shown promise in variational Monte Carlo algorithms by their theoretical capability of representing any quantum state. However, the reason behind the practical improvement in their performance with an increase in the number of parameters is not fully understood. In this work, we systematically study the efficiency of restricted Boltzmann Machines (RBMs) to represent the ground states in different phases of the spin-1 bilinear-biquadratic model, as the hidden layer density increases. We train our ansatz by minimizing two different loss functions: 1) energy, and 2) infidelity of the NQS ansatz w.r.t. that of the exact ground state. We observe that the accuracy of our ansatz saturates with in both cases. We demonstrate that this can be explained by looking at the spectrum of the quantum geometric tensor (QGT). We find that the rank of the QGT saturates beyond a certain , and we emphasize that it corresponds to the \textit{dimension of the relevant manifold} for an optimized NQS. This provides a useful diagnostics for the practical representation power of an NQS ansatz
Magnetized Strange Stars and Signals of Gravitational Waves
No full textInternational audienceWe study the emission of gravitational waves from spheroidal magnetized strange stars for both an isolated slowly rotating star and a binary system. In the first case, we compute the quadrupole moment and the amplitude of gravitational waves that may be emitted. For the binary system, the tidal deformability is obtained by solving simultaneously the system of spheroidal structure equations and the Love number equation. These results are compared with the data inferred from the GW170817 event which is also used to calculate the mass and tidal deformability of the companion star in the binary system. Our model supports binary systems formed by magnetized strange stars describing reasonable signals of gravitational waves contrasted with other models of binary systems composed of magnetized hadronic stars and non-magnetized quark stars
A mesh-independent method for second-order potential mean field games
No full textInternational audienceThis article investigates the convergence of the Generalized Frank-Wolfe (GFW) algorithm for the resolution of potential and convex second-order mean field games. More specifically, the impact of the discretization of the mean-field-game system on the effectiveness of the GFW algorithm is analyzed. The article focuses on the theta-scheme introduced by the authors in a previous study. A sublinear and a linear rate of convergence are obtained, for two different choices of stepsizes. These rates have the mesh-independence property: the underlying convergence constants are independent of the discretization parameters
On the stability of the invariant probability measures of McKean-Vlasov equations
No full textInternational audienceWe study the long-time behavior of some McKean-Vlasov stochastic differential equations used to model the evolution of large populations of interacting agents. We give conditions ensuring the local stability of an invariant probability measure. Lions derivatives are used in a novel way to obtain our stability criteria. We obtain results for non-local McKean-Vlasov equations on and for McKean-Vlasov equations on the torus where the interaction kernel is given by a convolution. On , we prove that the location of the roots of an analytic function determines the stability. On the torus, our stability criterion involves the Fourier coefficients of the interaction kernel. In both cases, we prove the convergence in the Wasserstein metric with an exponential rate of convergence.On étudie le comportement en temps long d’équations non-linéaires au sens de McKean–Vlasov. Ces équations sont utilisées pour modéliser les comportements de grandes populations d’agents en interaction. On donne des critères garantissant la stabilité locale d’une mesure de probabilité invariante. Pour ce faire, on utilise de manière novatrice les dérivées de Lions. On obtient des résultats pour des équations de McKean–Vlasov non locales sur , ainsi que pour des équations de McKean–Vlasov sur le tore pour lesquelles le noyau d’interaction est donné par une convolution. Sur , on montre que la stabilité est déterminée par l’emplacement des zéros d’une fonction holomorphe. Sur le tore, notre critère de stabilité fait intervenir les coefficients de Fourier du noyau d’interaction. Dans les deux cas, on montre la convergence vers la mesure de probabilité invariante à vitesse exponentielle pour la métrique de Wasserstein
Nakuru County Annual Development Plan 2026/2027
No full textThe Public Finance Management Act (PFMA), 2012, section 126, delineates the framework for county planning, which encompasses the formulation of various strategic plans, including the Annual Development Plans (ADPs). The ADP serves as the foundation for executing the County Integrated Development Plan (CIDP) and for directing resource allocation towards prioritized programs and projects. This process of developing the ADP disaggregates the priorities outlined in the CIDP into specific, short-term objectives that span one year. Furthermore, the ADP establishes a connection between county development priorities and broader national initiatives such as Kenya Vision 2030, its Medium-Term Plan IV (MTP IV), and the Bottom-Up Economic Transformation Agenda (BETA). The ADP 2026/2027 was developed through a collaborative and inclusive process involving all stakeholders, including the public, organized groups, professionals, development partners, and investors. Public participation forums were held across all sub-counties, ensuring that the contributions of all stakeholders were reflected in the plan. Moreover, inputs from various departmental Sector Working Groups (SWGs) augmented the priority areas and projects in the plan period. This methodological approach allowed for the identification of key programs and priorities that directly address the county's most pressing challenges and opportunities while ensuring that ongoing programs and projects are prioritized to achieve the set goals. This policy document focuses on prioritizing high-impact, transformative programs, sectoral interventions, and multi-year projects designed to enhance the well-being of Nakuru County residents. It highlights the County Government's dedication to improving healthcare by upgrading health infrastructure and increasing access to quality services. The plan also: emphasizes boosting agricultural productivity, promoting agribusiness & value chain; expanding and maintaining road networks; and providing affordable, quality Early Childhood Development Education & Vocational Training education through initiatives like the school feeding program and optimal recruitment of teachers. Additionally, the plan emphasizes the importance of ensuring access to potable water, promoting gender equity & inclusivity and creating a favourable environment for trade and sustainable economic development. In collaboration with the National Government, the plan outlines Affordable Housing Programs and strategies for digitizing building plan approvals to prevent leakages. Moreover, the ADP aims at the integration of National, Regional, and International Development Frameworks, Commitments and Obligations. It intends to capitalize on strengths and opportunities while addressing challenges that slow the county's progress. The execution of the Annual Development Plan (ADP) for the period 2026-2027 is anticipated to necessitate a total resource allocation of Ksh 23.8 billion to effectively finance the prioritized strategic interventions. This figure is in contrast to an expected Annual Development Plan 26.27 xi | P a g e revenue of Ksh 23.4 billion. Specifically, Ksh 16.7 billion will be allocated for recurrent expenditures, while Ksh 7.1 billion will be directed towards development expenditures
Uasin Gishu County Programme Based Budget 2025/2026
No full textThe Uasin Gishu County Annual Budget Estimates for the Financial Year 2025/2026 have been prepared pursuant to section 129(1) of the Public Finance Management Act, 2012, and within the framework of the 2025 County Fiscal Strategy Paper. The budget is also aligned to national objectives as highlighted in the Budget Policy Statement and took into consideration the views of the public as required by the Constitution of Kenya (CoK). The 2025/2026 budget has been prepared against the backdrop of a stable national economy as a result of easing global inflation and supply-chain restrictions. This growth was primarily supported by the strong performance in the agriculture sector, a slight recovery of the manufacturing sector, and the resilience of the services sector. Uasin Gishu County has also benefited from this growth potential, with its share of Gross County Product (GCP) rising to 2.5 percent in 2023, up from 2.4 percent the previous year. The budget preparation therefore reflects a strategic alignment with this broader economic trend and a vision for growth. The budget seeks to leverage this strong economic performance to deliver the Nguzo Kumi transformational agenda. Thus, the budget prioritizes completion and operationalization of all key Nguzo Kumi flagship projects initiated in the current financial year as well as new projects expected to deliver the promises of the Governor. In addition, the budget has complied with the 2025 County Fiscal Strategy Paper (CFSP), which prioritizes roads, followed by agriculture and agribusiness, water, health, education and vocational training, trade and cooperatives, lands and physical planning, and the City of Eldoret in that sequence. It will also bolster the business environment in the county through structural reforms in trade and investment and prepare a city development plan to tap into the anticipated opportunities for economic growth