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Strategic geometric graphs through mean field games
No full textInternational audienceWe exploit the structure of geometric graphs on Riemannian manifolds to analyze strategicdynamic graphs at the limit, when the number of nodes tends to infinity. This frameworkallows to preserve intrinsic geometrical information about the limiting graph structure, suchas the Ollivier curvature. After introducing the setting, we derive a mean field game system,which models a strategic equilibrium between the nodes. It has the usual structure withthe distinction of being set on a manifold. Finally, we establish existence and uniquenessof solutions to the system when the Hamiltonian is quadratic for a class of non-necessarilycompact Riemannian manifolds, referred to as manifolds of bounded geometry
Searches for Higgs boson production through decays of heavy resonances
No full textInternational audienceThe discovery of the Higgs boson has led to new possible signatures for heavy resonance searches at the LHC. Since then, search channels including at least one Higgs boson plus another particle have formed an important part of the program of new physics searches. In this report, the status of these searches by the CMS Collaboration is reviewed. Searches are discussed for resonances decaying to two Higgs bosons, a Higgs and a vector boson, or a Higgs boson and another new resonance, with proton-proton collision data collected at = 13 TeV in the years 2016-2018. A combination of the results of these searches is presented together with constraints on different beyond-the-standard model scenarios, including scenarios with extended Higgs sectors, heavy vector bosons and extra dimensions. Studies are shown for the first time by CMS on the validity of the narrow-width approximation in searches for the resonant production of a pair of Higgs bosons. The potential for a discovery at the High Luminosity LHC is also discussed
Review of top quark mass measurements in CMS
No full textInternational audienceThe top quark mass is one of the most intriguing parameters of the standard model (SM). Its value indicates a Yukawa coupling close to unity, and the resulting strong ties to the Higgs physics make the top quark mass a crucial ingredient for understanding essential aspects of the electroweak sector of the SM. While it is such an important parameter of the SM, its measurement and interpretation in terms of the Lagrangian parameter are challenging. The CMS Collaboration has performed multiple measurements of the top quark mass, addressing these challenges from different angles: highly precise `direct' measurements, using the top quark decay products, as well as `indirect' measurements aiming at accurate interpretations in terms of the Lagrangian parameter. Recent mass measurements using Lorentz-boosted top quarks are particularly promising, opening a new avenue of measurements based on top quark decay products contained in a single particle jet, with superior prospects for accurate theoretical interpretations. Moreover, dedicated studies of the dominant uncertainties in the modelling of the signal processes have been performed. This review offers the first comprehensive overview of these measurements performed by the CMS Collaboration using the data collected at centre-of-mass energies of 7, 8, and 13 TeV
On Cutting Planes for Signomial Programming
No full textaccepted for publication in SIAM Journal on OptimizationInternational audienceCutting planes are of crucial importance when solving nonconvex nonlinear programs to global optimality, for example using the spatial branch-and-bound algorithms. In this paper, we discuss the generation of cutting planes for signomial programming. Many global optimization algorithms lift signomial programs into an extended formulation such that these algorithms can construct relaxations of the signomial program by outer approximations of the lifted set encoding nonconvex signomial term sets, i.e., hypographs, or epigraphs of signomial terms. We show that any signomial term set can be transformed into the subset of the difference of two concave power functions, from which we derive two kinds of valid linear inequalities. Intersection cuts are constructed using signomial term-free sets which do not contain any point of the signomial term set in their interior. We show that these signomial term-free sets are maximal in the nonnegative orthant, and use them to derive intersection sets. We then convexify a concave power function in the reformulation of the signomial term set, resulting in a convex set containing the signomial term set. This convex outer approximation is constructed in an extended space, and we separate a class of valid linear inequalities by projection from this approximation. We implement the valid inequalities in a global optimization solver and test them on MINLPLib instances. Our results show that both types of valid inequalities provide comparable reductions in running time, number of search nodes, and duality gap
THE GLOBAL STABILITY OF THE KALUZA-KLEIN SPACETIME
No full textInternational audienceIn this paper we show the classical global stability of the flat Kaluza-Klein spacetime, which corresponds to Minkowski spacetime in R 1+4 with one direction compactified on a circle. We consider small perturbations which are allowed to vary in all directions including the compact direction. These perturbations lead to the creation of massless modes and Klein-Gordon modes. On the analytic side, this leads to a PDE system coupling wave equations to an infinite sequence of Klein-Gordon equations with different masses. The techniques we use are based purely in physical space using the vectorfield method
Topological Matter and Fractional Entangled Geometry
No full textInternational audienceHere, we review our progress on a geometrical approach of quantum physics and topological crystals starting from nature, electrodynamics of planets and linking with Dirac magnetic monopoles and gauge fields. The Bloch sphere of a quantum spin- particle can also acquire an integer topological charge in the presence of a radial magnetic field. We show that the global topological properties are revealed from the poles of the surface allowing a correspondence between smooth fields, metric and quantum distance. The information is transported from each pole to the equatorial plane on a thin Dirac string. We develop the theory, "the quantum topometry" in space and time, and present applications on transport from a Newtonian approach, on a quantized photo-electric effect from circular dichroism of light towards topological band structures of crystals. The occurrence of robust edge modes related to the topological lattice models are revealed analytically when deforming the sphere or ellipse onto a cylinder. The topological properties of the quantum Hall effect, the quantum anomalous Hall effect and the quantum spin Hall effect on the honeycomb lattice can be measured locally in the Brillouin zone from the light-matter coupling. The formalism allows us to include interaction effects from the momentum space. Interactions may also result in fractional entangled geometry within the curved space. We develop a relation between entangled wavefunction in quantum mechanics, coherent superposition of geometries, a way to one-half topological numbers and Majorana fermions. We show realizations in topological matter. We present a relation between axion electrodynamics, topological insulators on a surface of a cube and the two-spheres' model via the meron
West Pokot County Annual Development Plan 2025/2026
No full textThis Annual Development Plan presents the County Government priorities, proposals and development programmes for financial year 2025/26. The priorities under the plan have been anchored on the County Integrated Development Plan (2023-2027), Public Participation and validation reports for ADP, Bottom-Up Economic Transformation Agenda (BETA)and the Fourth Medium Term Plan of Kenya Vision 2030. The preparation of the Annual Development Plan FY 2025-2026, was an inclusive consultative and participatory by all stakeholders and Sector Working Groups. The plan takes into account the strategic priorities for the medium term that reflects the county government's priorities and plans and the ever changing financial and economic environment. The plan took also into consideration the implementation milestinoes, challenges and lessons learnt in FY 2023/24 as well as the preparation of FY 2024/25 budget. It Further link the running CADP FY 2024/25 with Budget.
The desired outcome of this plan is alleviation of the high poverty and illiteracy levels and to stimulate job creation and wealth for the county residents.The unveiling of the County Annual Development Plan is a clear demonstration of our commitment to the realization of our county vision of being the model county in service delivery
Homa Bay County Fiscal Strategy Paper 2025
Get PDFThe County Fiscal Strategy Paper 2025 is the third to be prepared under the Genowa Economic blueprint in line with section 117 of the PFM Act 2012 read together with the provisions of the county government act 2012 on planning. it outlines the progress made in the implementation of the county governments development agenda which seeks to maximize social, economic and political opportunities for benefit of the citizens. the interventions planned in the fiscal year 2025 will be anchored on the theme: consolidating the gains under the Genowa economic transformation for inclusive green growth. it is a commitment to steadily invest in and consolidate gains made in the following areas....................
Mandera County Budget Review and Outlook Paper 2025
Get PDFThis County Budget Review Outlook Paper (CBROP) was prepared as required by section 118 of the Public Finance Management Act, 2012. It reviews the actual fiscal performance of the financial year 2024/2025 and makes comparisons to the budget appropriations of the same year. It also provides the recent economic developments and the updated economic and financial forecast with sufficient information to show changes from the forecast in the County Fiscal Strategy Paper (CFSP) of February, 2025. In reviewing the fiscal performance, this paper analyzes the performance of County Own generated revenue in the FY 2024/2025. It has included the total revenue collected and made comparison to the budgeted revenue for the same year. In addition, possible causes of the underperformance in revenues are also highlighted. The paper also provides departmental expenditures for both recurrent and development for the year under review. A comparison of actual performance against targets for FY 2024/2025 is provided. The preparation of this CBROP will be an important tool that will help in the formulation of 2026/2027 budget and will also provide foundation for the 2026 CFSP. Through proper planning, the County Government of Mandera intends to achieve maximum fiscal discipline that ensures proper management of public resources and delivery of expected output. To ensure transparency and accountability, the County Executive will involve and relay budget performance and management reports to all county stakeholders as required by the constitution of Kenya, 2010 and Public Finance Management Act, 2012
Kiambu County Annual Development Plan 2025/2026
Get PDFThis tenth Kiambu County Annual Development Plan (CADP) marks a significant step in our journey under devolved governance. It is the third plan to be prepared under the County Integrated Development Plan (CIDP) 2023-2027, further solidifying our commitment to strategic and long-term development. In adherence to Section 126 of the Public Finance Management Act (PFMA), 2012, and Article 220(2) of the Constitution of Kenya, this plan outlines our medium-term strategic priorities, the programs we will deliver, and the associated financial commitments. It encompasses a broad spectrum of social and economic development issues, aligning with national and global agendas such as Vision 2030, the Sustainable Development Goals (SDGs), Agenda 2063, and the Bottom-Up Economic Transformation Agenda (BETA). It also reflects the promises made in the Governor's Manifesto. The CADP 2025-2026, derived from the CIDP, provides a detailed one-year roadmap with costed programs, clear objectives, and robust monitoring and reporting frameworks. It serves as the bedrock for budgeting and planning in the county. We are proud that this plan is a product of extensive collaboration and public participation. County departments, stakeholders, and residents all contributed their insights and aspirations, ensuring that the plan truly reflects the needs and priorities of our people. We extend our sincere gratitude to everyone who participated in this process