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    Overview of high-density QCD studies with the CMS experiment at the LHC

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    International audienceThe heavy ion (HI) physics program has proven to be an essential part of the overall physics program at the Large Hadron Collider at CERN. Its main purpose has been to provide a detailed characterization of the quark-gluon plasma (QGP), a deconfined state of quarks and gluons created in high-energy nucleus-nucleus collisions. From the start of the LHC HI program with lead-lead collisions, the CMS Collaboration has performed measurements using additional data sets in different center-of-mass energies with xenon-xenon, proton-lead, and proton-proton collisions. A broad collection of observables related to high-density quantum chromodynamics (QCD), precision quantum electrodynamics (QED), and even novel searches of phenomena beyond the standard model (BSM) have been studied. Major advances toward understanding the macroscopic and microscopic QGP properties were achieved at the highest temperature reached in the laboratory and for vanishingly small values of the baryon chemical potential. This article summarizes key QCD, QED, as well as BSM physics, results of the CMS HI program for the LHC Runs 1 (2010-2013) and 2 (2015-2018). It reviews findings on the partonic content of nuclei and properties of the QGP and describes the surprising QGP-like effects in collision systems smaller than lead-lead or xenon-xenon. In addition, it outlines the scientific case of using ultrarelativistic HI collisions in the coming decades to characterize the QGP with unparalleled precision and to probe novel fundamental physics phenomena

    Limite "annealed" pour un modèle champ-moyen, diffusif et désordonné avec des sauts aléatoires

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    International audienceWe study a sequence of NN-particle mean-field systems, each driven by NN simple point processes ZN,iZ^{N,i} in a random environment. Each ZN,iZ^{N,i} has the same intensity (f(XtN))t(f(X^N_{t-}))_t and at every jump time of ZN,i,Z^{N,i}, the process XNX^N does a jump of height Ui/NU_i/\sqrt{N} where the UiU_i are disordered centered random variables attached to each particle. We prove the convergence in distribution of XNX^N to some limit process Xˉ\bar X that is solution to an SDE with a random environment given by a Gaussian variable, with a convergence speed for the finite-dimensional distributions. This Gaussian variable is created by a CLT as the limit of the patial sums of the Ui.U_i. To prove this result, we use a coupling for the classical CLT relying on the result of [Koml\'os, Major and Tusn\'ady (1976)], that allows to compare the conditional distributions of XNX^N and Xˉ\bar X given the random environment, with the same Markovian technics as the ones used in [Erny, L\"ocherbach and Loukianova (2022)].Nous étudions une suite de systèmes de NN particules en champ-moyen, où chaque système est dirigé par NN processus ponctuels simples ZN,iZ^{N,i} dans un environnement aléatoire. Chaque Z^{N,i} a la même intensité f(XtN)tf(X^N_{t-})_t et à chaque instant de saut de ZN,i,,Z^{N,i,}, le processus XNX^N fait un saut d'amplitude Ui/NU_i/\sqrt{N}UiU_i sont des variables aléatoires de désordre centrées attachées à chaque particule. Nous prouvons la convergence en loi de XNX^N vers un processus limite Xˉ\bar X qui est solution d'une EDS dans un environnement aléatoire donné par une variable gaussienne, avec une vitesse de convergence pour les lois fini-dimensionelles. Cette variable gaussienne est créé par un TCL comme la limite des sommes partielles des Ui.U_i. Pour montrer ce résultat, nous utilisons un couplage pour le TCL classique qui repose sur le résultat de [Koml\'os, Major et Tusn\'ady (1976)], qui permet de comparer les lois conditionnelles de XNX^N et de Xˉ\bar X étant donné les variables d'environnement, avec les mêmes techniques markoviennes que celles utilisées dans [Erny, L\"ocherbach et Loukianova (2022)]

    Multi-parameter Module Approximation: an efficient and interpretable invariant for multi-parameter persistence modules with guarantees

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    International audienceTopological data analysis (TDA) is a rapidly growing area of data science, whose most common descriptor is persistent homology, which tracks the topological changes in growing families of subsets of the data set itself, called filtrations, and encodes them in an algebraic object, called a persistence module. The algorithmic and theoretical properties of persistence modules are now well understood in the single-parameter case, that is, when there is only one filtration (e.g., feature scale) to study. In contrast, much less is known in the multi-parameter case, where several filtrations (e.g., scale and density) are used simultaneously. Since multi-parameter persistence modules usually encode information that is invisible to their single-parameter counterparts, it is critical to build tractable proxies for them, ideally with some theoretical robustness guarantees. In this article, we introduce a new parameterized family of topological descriptors, taking the form of candidate decompositions, for multi-parameter persistence modules, and we a identify a subfamily of these descriptors, that we call approximate decompositions, that are controllable approximations, in the sense that they preserve diagonal barcodes. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm based on matching functions for computing instances of candidate decompositions with some precision parameter delta . By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Moreover, we prove the robustess of MMA: when computed with so-called compatible matching functions, we show that MMA produces approximate decompositions (and we prove that such matching functions exist for n = 2 filtrations). Next, we restrict the focus on modules that can be decomposed into interval summands. In that case, compatible matching functions always exist, and we show that, for small enough delta, the approximate decompositions obtained with such compatible matching functions by MMA have an approximation error (in terms of the standard interleaving and bottleneck distances) that is bounded by delta, and that reaches zero for an even smaller, positive precision delta_exact. Finally, we present empirical evidence validating that MMA has state-of-the-art performance and running time on several data sets

    Tharaka-Nithi County Annual Development Plan 2026/2027

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    The County Planning framework is guided by various legislative policies demonstrates a link between international, County Government and National Government obligations. As such, the commitments outlined in the County Government Act (CGA) 2012, bears the legal basis for the preparation of various county plans, including the procedures synonymous to county planning processes. Specifically, Part XI, Section 104 of the County Government Act, 2012, states that a county government shall plan for the county and no public funds shall be appropriated outside a planning framework developed by the County Executive Committee and approved by the county assembly. Further, Section 109 (1) of the CGA states that a Programme-based approach shall be adopted during budgeting and performance management. Additionally, section 113 postulates that County Integrated Development Plans should inform budget preparation and based on the annual development priorities and objectives. The Public Finance Management Act, 2012 section 126 provides further guidance, and states that each County prepare annual development plans in accordance with Article 220 (2) of the constitution of Kenya, 2010, and embodies county government priorities and plans. The 2026/2027 County Annual Development Plan (CADP) highlights strategic priorities and resource management approaches of the county and brings together cumulative achievements in line with the clarion call to leave no one behind. Therefore, this County Annual Development Plan has been prepared in accordance with plans outlined by the CIDP 2023-2027 aspirations highlighted by the people of Tharaka Nithi. This CADP has carefully considered important factors such as future planning for projects identified in accordance with the national planning framework and recommendations as indicated by international commitments and obligations. The plan prioritizes sector working group reports as well as an analysis of priority goals outlined during the budget cycle and planning processes. The proposals for the eight (8) sectors within the County Government have informed the priorities in each Programme in addition to projects, with a bias to those that are currently underway and posing fair consideration to new projects that will provide substantial impact to a majority of residents. The planning process has therefore continued to pursue excellence in the process of ensuring effective service delivery and fortifying departmental operations through providing financial and human resource planning for implementation of County goals and objectives. The 2026/2027 CADP provides guidelines on the implementation, monitoring and evaluation framework informed by strategic management principles for each intervention. The success of this plan therefore calls for unity of purpose and support among all stakeholders

    Garrissa County Annual Development Plan 2026/2027

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    Sections 104, 105 and 108 of the County Government Act, 2012 provides that County Governments are responsible for the preparation of the integrated development plans which guides integrated planning within their counties taking into consideration the linkages between county plans, the national planning framework and meaningful engagement of citizens in the planning process through collection, collation, storage and updating of data and information suitable for the planning processes. In addition, the Public Finance Management Act (PFMA), 2012 outlines the county planning framework which provides for the preparation of various plans that includes the Annual Development Plans (ADPs). The ADP provides the basis for implementation of the County Integrated Development Plan (CIDP 2023-2027) and acts as a guide in resource allocation to priority programmes and projects for the FY 2026-2027. The preparation of this document involved working closely with the County Sector Working Groups (SWGs), incorporating inputs shared by the members of the public, development partners and the County Executive Committee Members. Further, the finalization of this Plan referred to key County/National Government Policy documents particularly the Garissa County Integrated Development Plan (2023-2027), the Bottom up economic transformation agenda (BETA), the Medium-Term Plan-MTP IV (2023 – 2027) of the Vision 2030 and the governor’s manifesto. This plan provides for a monitoring and evaluation matrix which guides departments while tracking the implementation progress of the priority programmes/projects in a bid to promote informed and evidenced-based decision-making in the County. I believe, successful implementation of the programmes and projects will contribute to a better delivery of county services, employment creation, faster economic growth, as well as poverty reduction

    Vihiga County Agroecology Policy 2025

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    Agriculture is an important aspect within Kenya’s economy as it contributes directly to about 33% of its GDP and 25% indirectly through linkages with other sectors (FAO, 2023). Despite being a leading aspect in the country’s economic drive, the sector still faces a myriad of challenges that ends up affecting its food systems. This policy document highlights some of the key identifiable challenges, with specific emphasis on the Vihiga County ecosystem, while recommending various interventions that needs to be adopted in the sector to attain a sustainable food system for the rural communities. The policy document contains four chapters. The first chapter revolves around how the agricultural sector is a major contributor to the economic growth of the country as it highlights some of the prevailing challenges being faced such as land degradation, declining soil health, food insecurity, unemployment, low incomes, and rural-urban migration. The second chapter focuses on the current situation being faced in Vihiga County concerning its Agri-food system, with complex challenges such as inadequate germplasm, land fragmentation, high population density, low agricultural productivity, poor agricultural diversity, among other factors at play

    Speech by His Excellency President William Samoei Ruto, Phd., C.G.H on Labour Day May 1, 2025

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    President William Ruto’s 2025 Labour Day address highlights Kenya’s progress in strengthening workers’ welfare, economic self-reliance, and national productivity, centred around the theme “Self-Reliance in Production is the Key to Economic Growth.” He outlines major reforms in the 2025 Finance Bill—including direct application of PAYE reliefs, tax-exempt pensions, and simplified taxation for small businesses—alongside transformative gains in national savings driven by enhanced NSSF contributions, which have mobilised KSh280 billion in two years. The President reports strong advances under the Bottom-Up Economic Transformation Agenda: increased agricultural output due to fertilizer affordability, revitalised coffee and sugar sectors, over 250,000 jobs created through affordable housing, and expanded MSME support through the Hustler Fund. He further highlights hiring of 76,000 teachers, growing labour migration opportunities, and expanded healthcare coverage with 21 million people registered under the Social Health Authority. Ruto concludes by reaffirming workers’ rights, directing protection for unionisation, and announcing Kenya’s plan to ratify ILO Conventions 189 and 190

    Garissa County Fiscal Strategy Paper 2025

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    The Garissa County Fiscal Strategy Paper (CFSP) 2025 has been prepared in accordance with Section 117(1) and (6) of the Public Finance Management (PFM) Act, 2012, and Section 26 of the Public Finance Management (County Governments) Regulations, 2015. It outlines the fiscal policy direction for the 2025/2026 budget and sets the budgetary priorities for the third year of the County Integrated Development Plan (CIDP) 2023-2027. This document defines the county’s fiscal policy framework, detailing economic priorities, financial projections, budget allocations, and strategic initiatives aimed at fostering sustainable economic growth and development. The CFSP is aligned with the Approved Budget Policy Statement (BPS) 2024/2025, ensuring responsible fiscal management, transparency, and accountability. The paper provides an analysis of the global and national economic landscape and its implications for Garissa County’s economy. It highlights the county’s economic strengths, challenges, and opportunities, focusing on key sectors such as agriculture, trade, and tourism. Given the potential impact of external economic shocks, the strategy underscores the importance of resilience and adaptability. It also reviews the county’s fiscal performance in the past financial year, including revenue collection trends, expenditure patterns, and budget execution rates. Additionally, the document outlines future revenue projections and expenditure priorities, emphasizing fiscal discipline and efficient resource allocation to align spending with strategic objectives

    Turkana County Fiscal Strategy Paper 2025

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    The Turkana County Fiscal Strategy Paper (CFSP) 2025 is a policy document which has outlined strategic priorities and policy goals for the progressive realisation of H.E Governor Jeremiah Ekamais Lomorukai Napotikan’s 9-Point Agenda with emphasis on food security, water as a universal right, revenue enhancement, public private partnerships, health care, education and partnerships building over the medium-term period. The document generally sets out the county’s sectoral policy goals and strategic priorities which will be the basis for the formulation of the County’s Financial Year 2025/2026 budget estimates expenditure, revenues and the medium-term projections. These priorities are based on and have been outlined in the Annual Development Plan (ADP) 2025-2026, the third generation County Integrated Development Plan (CIDP) 2023-2027, the Medium Term Plan (MTP) IV ,the Bottom-up Economic Transformation Agenda ( BETA) and the Kenya Vision 2030. The paper is a build-up on the County Budget Review and Outlook Paper (CBROP) 2024, wherefrom the performance of the previous FY 2023/2024 has been examined and reviewed. The document has furthermore given a global and local medium term outlook in addition to providing sector budget ceilings that will inform budget estimates for the next financial year. The main sources of the county’s revenue for the next financial year and in the medium term, is expected to be equitable share, conditional grants, local revenue collections and development partners donor funding. According to the Commission on Revenue Allocation recommendation and the draft County Allocation of Revenue Bill 2025, Turkana County is expected to receive approximately KES 13.8 billion as Equitable Share though the Fourth basis framework formular used to allocate revenue to counties is currently under contestation. The Own Source Revenue is expected to be in the region of KES 380M. We expect to receive grants worth KES 2.99 billion from development partners. The expected revenue is not adequate enough to fund the priorities for next financial year as outlined in the Sector Working Group reports. According to the resource requirements for all sectors, we require approximately KES 28.3 billion to fund sectors priorities yet we anticipate to receive KES 17.1 billion, implying a glaring deficit of KES 11.2 billion. We have prioritized completion and operationalization of stalled projects spread across the County and the County Treasury has proposed a ward development allocation of KES 1.5 billion for the completion of these projects . We are minimizing creation of new projects because Equalization fund and other development partners are creating and implementing new projects across all wards .We shall continue with progressive payments of accumulated pending bills that have been verified and audited. We have allocated KES 750 Million for the settlement of pending bills. We have provided resources for grants counter funding. We have allocated and ring fenced resources for the provision of the most critical goods and services. We have allocated KES 320M for Lodwar Level B Hospital, which is an ongoing multi year flagship project. The recent suspension of the USAID aid programmes is expected to result into increased demand for more resources allocation to the medical sector to plug in the gap in terms of personnel costs, medical supplies, nutrition, WASH and medical facilities operation

    Samburu County Fiscal Strategy Paper 2025

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    The preparation of the CFSP 2025 was a consultative process that involved seeking and considering the views of The Commission on Revenue Allocation; The National Treasury; the public and interested Stakeholders. The County Fiscal Strategy Paper contains: The performance section provides up-to-date information on county government expenditure and revenue collection. It helps to determine whether the decisions made going forward on revenue collection and expenditure are realistic The projections which indicate the overall revenue and expenditure expected for 2025/26 budget year. The Priorities which deal with identifying what to fund or the distribution of needs across sectors. The ceillings which determine the amount of money allocated to each sector and how the money is distributed across sectors. The ceilings should show the amount of money the county will spend on meeting the identified priorities The fiscal responsibility principles and financial objectives over the Medium Term

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