Podcasts about unified framework

Meet Joe Sanok Joe Sanok helps counselors to create thriving practices that are the envy of other counselors. He has helped counselors to grow their businesses by 50-500% and is proud of all the private practice owners who are growing their income, influence, and impact on the world. Click here to explore consulting with Joe. […] The post Mindfulness, Chocolate, and a Unified Framework for Psychotherapy – Insights from Dr. Diane Gehart | POP 1156 appeared first on How to Start, Grow, and Scale a Private Practice | Practice of the Practice.

Large Language Models (LLMs) demonstrate human-level capabilities in dialogue, reasoning, and knowledge retention. However, even the most advanced LLMs face challenges such as hallucinations and real-time updating of their knowledge. Current research addresses this bottleneck by equipping LLMs with external knowledge, a technique known as Retrieval Augmented Generation (RAG). However, two key issues constrained the development of RAG. First, there is a growing lack of comprehensive and fair comparisons between novel RAG algorithms. Second, open-source tools such as LlamaIndex and LangChain employ high-level abstractions, which results in a lack of transparency and limits the ability to develop novel algorithms and evaluation metrics. To close this gap, we introduce RAGLAB, a modular and research-oriented open-source library. RAGLAB reproduces 6 existing algorithms and provides a comprehensive ecosystem for investigating RAG algorithms. Leveraging RAGLAB, we conduct a fair comparison of 6 RAG algorithms across 10 benchmarks. With RAGLAB, researchers can efficiently compare the performance of various algorithms and develop novel algorithms. 2024: Xuanwang Zhang, Yunze Song, Yidong Wang, Shuyun Tang, Xinfeng Li, Zhengran Zeng, Zhen Wu, Wei Ye, Wenyuan Xu, Yue Zhang, Xinyu Dai, Shikun Zhang, Qingsong Wen https://arxiv.org/pdf/2408.11381

Jailbreak attacks are crucial for identifying and mitigating the security vulnerabilities of Large Language Models (LLMs). They are designed to bypass safeguards and elicit prohibited outputs. However, due to significant differences among various jailbreak methods, there is no standard implementation framework available for the community, which limits comprehensive security evaluations. This paper introduces EasyJailbreak, a unified framework simplifying the construction and evaluation of jailbreak attacks against LLMs. It builds jailbreak attacks using four components: Selector, Mutator, Constraint, and Evaluator. This modular framework enables researchers to easily construct attacks from combinations of novel and existing components. So far, EasyJailbreak supports 11 distinct jailbreak methods and facilitates the security validation of a broad spectrum of LLMs. Our validation across 10 distinct LLMs reveals a significant vulnerability, with an average breach probability of 60% under various jailbreaking attacks. Notably, even advanced models like GPT-3.5-Turbo and GPT-4 exhibit average Attack Success Rates (ASR) of 57% and 33%, respectively. We have released a wealth of resources for researchers, including a web platform, PyPI published package, screencast video, and experimental outputs. 2024: Weikang Zhou, Xiao Wang, Limao Xiong, Han Xia, Yingshuang Gu, Mingxu Chai, Fukang Zhu, Caishuang Huang, Shihan Dou, Zhiheng Xi, Rui Zheng, Songyang Gao, Yicheng Zou, Hang Yan, Yifan Le, Ruohui Wang, Lijun Li, Jing Shao, Tao Gui, Qi Zhang, Xuanjing Huang https://arxiv.org/pdf/2403.12171v1.pdf

This episode is different in a few notable ways. First, it's extemporaneous. Second, I recorded it to video for release on my fledgling YouTube channel, where all of my past episodes currently reside. Finally, I share news about the future of the podcast–an ending to make way for a new beginning.  Key moments in this episode include: 00:00:01 - Embracing Change and New Beginnings 00:03:24 - Pursuing a Unified Framework 00:08:07 - Making Bold Choices 00:11:10 - Moving Forward with Conviction 00:13:48 - Seeking Audience Input Remember, you ARE going to die. But you're not dead yet. So get after it!   Let's Connect Find me on Facebook, Instagram and LinkedIn, visit my website, or email me.     Follow Andrew Petty is Dying & Leave a Review Apple Podcasts | Spotify | Google Podcasts | Stitcher   If You Liked This Episode, I Think You'll Like These, Too Ep. 022 | Tune Out to Tune In: Hearing & Heeding Your Inner Voice in a World Full of Noise Ep. 032 | Reimagining Productivity: A Path to Greater Freedom and Fulfillment

D'Angelo, Egidio, und Stefano Casali. „Seeking a Unified Framework for Cerebellar Function and Dysfunction: From Circuit Operations to Cognition“. Frontiers in Neural Circuits 6 (2013). https://doi.org/10.3389/fncir.2012.00116.

Multimodal learning aims to build models that can process and relate information from multiple modalities. Despite years of development in this field, it still remains challenging to design a unified network for processing various modalities ($textit{e.g.}$ natural language, 2D images, 3D point clouds, audio, video, time series, tabular data) due to the inherent gaps among them. In this work, we propose a framework, named Meta-Transformer, that leverages a $textbf{frozen}$ encoder to perform multimodal perception without any paired multimodal training data. In Meta-Transformer, the raw input data from various modalities are mapped into a shared token space, allowing a subsequent encoder with frozen parameters to extract high-level semantic features of the input data. Composed of three main components: a unified data tokenizer, a modality-shared encoder, and task-specific heads for downstream tasks, Meta-Transformer is the first framework to perform unified learning across 12 modalities with unpaired data. Experiments on different benchmarks reveal that Meta-Transformer can handle a wide range of tasks including fundamental perception (text, image, point cloud, audio, video), practical application (X-Ray, infrared, hyperspectral, and IMU), and data mining (graph, tabular, and time-series). Meta-Transformer indicates a promising future for developing unified multimodal intelligence with transformers. Code will be available at https://github.com/invictus717/MetaTransformer 2023: Yiyuan Zhang, Kaixiong Gong, Kaipeng Zhang, Hongsheng Li, Y. Qiao, Wanli Ouyang, Xiangyu Yue https://arxiv.org/pdf/2307.10802v1.pdf

Link to bioRxiv paper: http://biorxiv.org/cgi/content/short/2023.06.27.546746v1?rss=1 Authors: Schubert, J., Gehmacher, Q., Schmidt, F., Hartmann, T., Weisz, N. Abstract: Auditory speech comprehension is a multi-faceted process in which attention, prediction, and sensorimotor integration (via active sensing) interact with or complement each other. Although different conceptual models that focus on one of these aspects exist, we still lack a unified understanding of their role in speech processing. Here, we replicated and extended two recently published studies from our lab to investigate the influence of prediction tendency on ocular and neural tracking of attended speech. We propose that selective attention guides ocular speech tracking, which in turn mediates neural encoding of speech. In contrast, individual prediction tendency and its relation to neural speech tracking seem to be largely independent of attention. Importantly, prediction tendency and ocular speech tracking seem to be unrelated. With the current work, we propose a framework that aims to bridge the gaps between attention, prediction, and active (ocular) sensing in order to contribute to a holistic understanding of neural speech processing. Copy rights belong to original authors. Visit the link for more info Podcast created by Paper Player, LLC

Warren Powell is Chief Analytics Officer of Optimal Dynamics and Professor Emeritus from Princeton University, where he taught and served as a faculty member in the Department of Operations Research and Financial Engineering since 1981.  In the 1980s Powell designed and wrote SYSNET, an interactive optimization model for load planning at Yellow Freight System, where it is still in use after 25 years. He is the founder of Princeton Transportation Consulting Group, which marketed the model as SuperSPIN, stabilizing an industry where 80% of companies went bankrupt in the first post-deregulation decade. SuperSPIN was used in the planning of American Freightways (which became FedEx Freight) and Overnight Transportation (which became UPS Freight). In 1990 Powell founded CASTLE Laboratory which spans research in computational stochastic optimization with applications initially in transportation and logistics. In 2011 he then founded the Princeton laboratory for ENergy Systems Analysis (PENSA) to tackle the rich array of problems in energy systems analysis, and in 2013: this morphed into “CASTLE Labs,” focusing on computational stochastic optimization and learning. In 2017 Powell founded Optimal Dynamics, helping carriers to automate and optimize trucking networks using AI.  Motivated by these applications, he developed a method for bridging dynamic programming with math programming to solve very high-dimensional stochastic, dynamic programs using the modeling and algorithmic framework of approximate dynamic programming. He identified four fundamental classes of policies for solving sequential decision problems, integrating fields such as stochastic programming, dynamic programming (including approximate dynamic programming/reinforcement learning), robust optimization, optimal control and stochastic search (to name a few). This work identified a new class of policy called a parametric cost function approximation. His work in industry is balanced by contributions to the theory of stochastic optimization, and machine learning.

伏線回収、円安・オイル高騰中の海外生活・学会参加に関する雑談など。後半は、SNcドパミン神経の細胞体と軸索＠線条体の活動をサブタイプ毎に観察した仕事、カリウム選択的なチャネルロドプシンに関する論文×２、Eve Marderのエッセイを元にしたディスカッション（7/16収録） Show Notes: コロナ中に収録したエピソードその１ その２ Mark Anderman のパートナー、Maria Lehtinen David Kleinfeld 細胞そのものがセンサー(CNiFERs) Dombeckラボ Awatramaniラボ 論文１：Dopaminergic axons track somatic signaling in behaving mice Joshua Berke のラボから出ていたVTAの細胞体とNAcドパミンのdissociation アセチルコリンがドパミンの軸索でAction Potentialを起こす Amatramaniラボからの前報で、SNcドパミンの形態を細胞種毎にキャラクタライズした仕事 Dombeck は Striatum で single axon の2pイメージングやってた GRINレンズ２個刺しの仕事 RPE: Reward prediction error, 古典的レビューはこちら Kim et al., 論文 A Unified Framework for Dopamine Signals across Timescales 論文２：Kalium channelrhodopsins are natural light-gated potassium channels that mediate optogenetic inhibition John Spudich 普通のカリウムチャネルが持っているような選択フィルター 元論文 今週NNに出ていたAxon Terminal inhibitionのレビュー 論文３：WiChR, a highly potassium selective channelrhodopsin for low-light two-photon neuronal inhibition Peter Hegemann Emiliani Emotional Circuitのdevelopment Eve Marder エッセイのシリーズ：Living Science エッセイ１：Maintaining the joy of discovery エッセイ２：Crossing oceans Editorial Notes: Sodium とナトリウム、Potassiumとカリウムが混ざりました（宮脇） エスプレッソマシン、むかし友人を説得して業務用の中ではお手頃なシモネリのオスカーを買わせて一緒に遊んだりしてたのですが、洗浄が面倒すぎて一瞬で売り飛ばしていました笑 ところでロブスターを実験動物に使うと食べ放題だろうか。(萩原)

This week on The Encrypted Economy, my guest is John Verry. John is the Founder of Pivot Point Security, as well as the host of his own podcast called The Virtual CISO. He helps organizations of all shapes and sizes become certified in accordance with leading security frameworks like ISO 27001, and the new CMMC standard. John also specializes in reading the tea leaves when it comes to the futures of third-party risk management, and information security as a whole. It was a pleasure to talk to him about common security misconceptions and the potential for CMMC to unify the framework landscape. Do not miss this episode of The Encrypted Economy and keep an eye on The Virtual CISO Podcast where I will be making my own guest appearance! Topics Covered John's Background  Working for Small vs Large Clients  Changing Attitudes in Organizational Security  Product vs Framework vs Technically Focused Organizations  The False Sense of Security Brought by Tools The Importance of CMMC  IntegratingTheFramework Landscape  The Path Towards a Unified Framework  Adding Privacy to the Equation Resource List John's LinkedIn Pivot Point Security Website The Virtual CISO Podcast NYS DFS Cybersecurity 20 CIS Controls and Resources CIS Critical Security Controls Office 365 Security and Compliance The CMMC ISO 27001 NIST Cybersecurity Framework NIST SP 800-171 What is CUI? DOD's New CMMC Requirement GSA Polaris Draft Defense Federal Acquisition Regulation Supplement (DFARS) SOC 1 SOC 2 FedRamp FAIR Risk Management Framework NIST Privacy Framework California SB 327 

Taxes: We all hate them but we all have to pay them. In December 2017, the Republicans in Congress rushed major changes to our tax policy into law. In this episode, host Jen Briney and her accountant friend, Alexis Claypool, explain the most significant changes to how our tax payments are going to be calculated and how these changes are likely to affect us. You will also learn about a major dingleberry that hitchhiked its way into law attached to this bill. Joe Briney joins Jen for the Thank Yous. Please Support Congressional Dish - Quick Links Click here to contribute a lump sum or set up a monthly contribution via PayPal Click here to support Congressional Dish for each episode via Patreon Send Zelle payments to: Donation@congressionaldish.com Send Venmo payments to: @Jennifer-Briney Use your bank’s online bill pay function to mail contributions to: 5753 Hwy 85 North Number 4576 Crestview, FL 32536 Please make checks payable to Congressional Dish Thank you for supporting truly independent media! H.R. 1: An Act to provide for reconciliation pursuant to titles II and V of the concurrent resolution on the budget for fiscal year 2018.   Subtitle A - Individual Tax Reform Part I - Tax Rate Reform Sec. 11001. Modification of Rates Married Individuals Filing Joint Returns Heads of Households Unmarried Individuals Inflation Adjustment Part II - Deduction for Qualified Business Income of Pass-Thru Entities Sec. 11011. Deduction for Qualified Business Income Phase-In of Limit for Certain Taxpayers Qualified Business Income Exception for specified service businesses based on taxpayer's income Threshold Amount Application to partnerships and S Corporations Part III - Tax Benefits for Families and Individuals Sec. 11021. Increase in Standard Deduction Sec. 11022. Increase in and Modification of Child Tax Credit. Sec. 11027. Temporary Reduction in Medical Expense Deduction Floor. Special Rules for Use of Retirement Funds with Respect to Areas Damaged by 2016 Disasters Part IV - Education Part V - Deductions and Exclusions Sec. 11042. Limitation on Deduction for State and Local, etc. Taxes Sec. 11043. Limitation on Deduction for Qualified Residence Interest Sec. 11045. Suspension of Miscellaneous Itemized Deductions Sec. 11047. Suspension of Exclusion for Qualified Bicycle Commuting Reimbursement Sec. 11048. Suspension of Exclusion for Qualified Moving Expense Reimbursement Sec. 11049. Suspension of Deduction for Moving Expenses Sec. 11051. Repeal of Deduction for Alimony Payments Part VI - Increase in Estate and Gift Tax Exemption Sec. 11061. Increase in Estate and Gift Tax Exemption Part VII - Extension of Time Limit for Contesting IRS Levy Part VIII - Individual Mandate Sec. 11081. Elimination of Shared Responsibility of Payment for Individuals Failing to Maintain Minimum Essential Coverage Subtitle B - Alternative Minimum Tax Sec. 12001. Repeal of Tax for Corporations Sec. 12003. Increased Exemption for Individuals Subtitle C - Business-related Provisions Part I - Corporate Provisions Sec. 13001. 21-Percent Corporate Tax Rate Part II - Small Business Reforms Sec. 1301. Modifications of Rules for Expensing Depreciable Business Assets Part III - Cost Recovery and Accounting Methods Sec. 13201. Temporary 100-Percent Expensing for Certain Business Assets Sec. 13202. Modifications to Depreciation Limitations on Luxury Automobiles and Personal Use Property Part IV - Business-Related Exclusions and Deductions Sec. 13301. Limitation on Deduction for Interest Sec. 13304. Limitation on Deduction by Employers of Expenses for Fringe Benefits Qualified Transportation Fringes Transportation and Commuting Benefits Sec. 13306. Denial of Deduction for Certain Fines, Penalties, and Other Amounts Sec. 13307. Denial of Deduction for Settlements Subject to Nondisclosure Agreements Paid in Connection with Sexual Harassment or Sexual Abuse Sec. 13308. Repeal of Deduction for Local Lobbying Expenses Sec. 13311. Elimination of Deduction for Living Expenses Incurred by Members of Congress Part V - Business Credits Sec. 13403. Employer Credit for Paid Family and Medical Leave Termination Part VI - Provisions Related to Specific Entities and Industries Sec. 13531. Limitation on Deduction for FDIC Premiums Part VII - Employment Sec. 13602. Excise Tax on Excess Tax-Exempt Organization Executive Compensation Part VII - Exempt Organizations Sec. 13702. Excise Tax Based on Investment Income of Private Colleges and Universities Part IX - Other Provisions Sec. 13802. Reduced Rate of Excise Tax on Beer Sec. 13804. Reduced Rate of Excise Tax on Wine Sec. 13807. Reduced Rate of Excise Tax on Certain Distilled Spirits Subtitle D - International Tax Provisions Part 1 - Outbound Transactions Sec. 14101. Deduction for Foreign-Source Portion of Dividends Received by Domestic Corporations from Specified 10-Percent Owned Foreign Corporations Sec. 14202. Deduction for Foreign-Derived Intangible Income and Global Intangible Low-Taxed Income Sec. 14211. Elimination of Inclusion of Foreign Base Company Oil Related Income Part II - Inbound Transactions Part III - Other Provisions Title II Sec. 20001. Oil and Gas Program Sec. 20003. Strategic Petroleum Reserve Drawdown and Sale Additional Reading Article: Tax reform eliminates deduction for moving expenses by Brittany Benson, H&R Block, October 24, 2018. Article: What are political or lobbying expenses and are they deductible? by Jean Murray, The Balances MB, October 23, 2018. Article: What changes has the IRS made to moving expense reimbursement? by Terry Sheridan, Accounting Web, October 3, 2018. Article: How the Trump tax law passed: GOP adds sweeteners by The Hill Staff, The Hill, September 28, 2018. Article: Repatriated profits total $465 billion after Trump tax cuts - leaving $2.5 trillion overseas by Jeffry Bartash, MarketWatch, September 19, 2018. Article: Foreign-derived intangible income deduction: Tax reform's overlooked new benefit for U.S. corporate exporters by Frank J. Vari, The Tax Adviser, August 2, 2018. Article: Will the Tax Act set back private equity? by David Dayen, The American Prospect, July 2, 2018. Article: The new tax form is postcard-size, but more complicated than ever by Jim Tankersley, The New York Times, June 25, 2018. Article: Four key changes for depreciation deductions by Bobby M. Bragg, Jamison Money Farmer PC, May 29, 2018. Article: New: IRS announces 2018 tax rates, standard deductions, exemption amounts and more by Kelly Phillips Erb, Forbes, March 7, 2018. Article: New excise tax on excess executive compensation by tax-exempt organizations by Christine Faris and Stephen Sutten, Baker Tilly, January 29, 2018. Article: Tax credit aims to boost availability of paid family leave, but will it work? by Michelle Andrews, NPR, January 23, 2018. Article: Corporate America celebrated tax cuts by laying off workers by David Dayen, Vice, January 10, 2018. Article: Andy Blunt joining in lobbying venture wtih long-time confidant of his father by Chuck Raasch, St. Louis Post-Dispatch, January 10, 2018. Article: Bonus tucked into GOP tax bill for those aiming to deduct medical expenses by Michelle Andrews, Kaiser Health News, December 22, 2017. Article: Final tax bill includes huge estate tax win for the rich: The $22.4 million exemption by Ashlea Ebeling, Forbes, December 21, 2017. Article: Newly passed Tax Cuts and Jobs Act eliminates employers' commuter benefits deductions by Matt Gerard, NBS, December 21, 2017. Article: Beer, wine, and spirits industries toast passage of GOP tax bill by Victor I. Nava, Washington Examiner, December 20, 2017. Article: A quick guide to the GOP tax plan, Bloomberg News, December 18, 2017. Article: CEOs aren't waiting for the tax bill to pass - they've already started pocketing the windfall by David Dayen, The Intercept, December 18, 2017. Article: Have you ever felt sorry for the I.R.S.? Now might be the time by Patricia Cohen, The New York Times, December 18, 2017. Article: File your taxes on a postcard? A G.O.P. promise marked undeliverable by Jim Tankersley, The New York Times, December 16, 2017. Article: Special giveaways in tax cut bill benefit family members and colleagues of key GOP senators by Lee Fang, The Intercept, December 1, 2017. Article: CBO: Senate tax bill would hurt poor by Mallory Shelbourne, The Hill, November 27, 2017. Article: Republican plan delivers permanent corporate tax cut by Jim Tankersley, Thomas Kaplan, and Alan Rappeport, The New York Times, November 2, 2017. Article: The GOP Tax Bill is out - and now we know why it was secret for so long by David Dayen, The Nation, November 2, 2017. Article: BP's $20.8 billion gulf spill settlement nets $15.3 billion tax write-off by Robert W. Wood, Forbes, October 6, 2015. Resources CDC: Alcohol and Public Health Govtrack: H.R. 1: Tax Cuts and Jobs Act Institute on Taxation and Economic Policy: Who Pays? Joint Committee on Taxation Publication: JX-67-17 OpenSecrets.org: Dan Sullivan OpenSecrets.org: Don Young OpenSecrets.org: Lisa Murkowski OpenSecrets.org: Rep. Mike Kelly OpenSecrets.org: Rep. Peter DeFazio OpenSecrets.org: Sen. Rob Portman OpenSecrets.org: Sen. Roy Blunt Treasury.gov: Unified Framework for Fixing Our Broken Tax Code Turbo Tax: What Are Standard Tax Deductions? USGS: ANWR Maps Sound Clip Sources Congressional Record of the 115th Congress; House of Representatives, Wednesday, September 27, 2017. Congressional Record of the 115th Congress; House of Representatives, Thursday, September 28, 2017. Congressional Record of the 115th Congress; House of Representatives, Wednesday, October 4, 2017. Congressional Record of the 115th Congress; House of Representatives, Monday, December 18, 2017. Congressional Record of teh 115th Congress; House of Representatives, Tuesday, December 19, 2017. Community Suggestions See more Community Suggestions HERE. Cover Art Design by Only Child Imaginations Music Presented in This Episode Intro & Exit: Tired of Being Lied To by David Ippolito (found on Music Alley by mevio)

The current proposed tax reform changes may be the biggest changes to the Tax Code the country has seen since the mid 1980’s. To date, the government has been very light on details when it comes to proposed tax reform.  In late September the government released their “ Unified Framework for Fixing Our Broken Tax Code” outlining a little more detail on the potential changes being considered. In this podcast we review the key elements of the tax reform proposal and how those changes may impact you. Learn more about tax reform in this podcast:

Discussing the Unified Framework for Fixing Our Broken Tax Code by WealthCounsel

This episode discusses the Born-Infeld model for Electromagnetodynamics. Here, the standard model are the Maxwell equations coupling the interaction of magnetic and electric field with the help of a system of partial differential equations. This is a well-understood classical system. But in this classical model, one serious drawback is that the action of a point charge (which is represented by a Dirac measure on the right-hand side) leads to an infinite energy in the electric field which physically makes no sense. On the other hand, it should be possible to study the electric field of point charges since this is how the electric field is created. One solution for this challenge is to slightly change the point of view in a way similar to special relativity theory of Einstein. There, instead of taking the momentum () as preserved quantity and Lagrange parameter the Lagrangian is changed in a way that the bound for the velocity (in relativity the speed of light) is incorporated in the model. In the electromagnetic model, the Lagrangian would have to restrict the intensity of the fields. This was the idea which Borne and Infeld published already at the beginning of the last century. For the resulting system it is straightforward to calculate the fields for point charges. But unfortunately it is impossible to add the fields for several point charges (no superposition principle) since the resulting theory (and the PDE) are nonlinear. Physically this expresses, that the point charges do not act independently from each other but it accounts for certain interaction between the charges. Probably this interaction is really only important if charges are near enough to each other and locally it should be only influenced by the charge nearest. But it has not been possible to prove that up to now. The electrostatic case is elliptic but has a singularity at each point charge. So no classical regularity results are directly applicable. On the other hand, there is an interesting interplay with geometry since the PDE occurs as the mean curvature equation of hypersurfaces in the Minkowski space in relativity. The evolution problem is completely open. In the static case we have existence and uniqueness without really looking at the PDEs from the way the system is built. The PDE should provide at least qualitative information on the electric field. So if, e.g., there is a positive charge there could be a maximum of the field (for negative charges a minimum - respectively), and we would expect the field to be smooth outside these singular points. So a Lipschitz regular solution would seem probable. But it is open how to prove this mathematically. A special property is that the model has infinitely many inherent scales, namely all even powers of the gradient of the field. So to understand maybe asymptotic limits in theses scales could be a first interesting step. Denis Bonheure got his mathematical education at the Free University of Brussels and is working there as Professor of Mathematics at the moment. Literature and additional material M. Kiessling: Electromagnetic Field Theory Without Divergence Problems 1, The Born Legacy, Journal of Statistical Physics, Volume 116, Issue 1, pp 1057-1122, 2004. M. Kiessling: Electromagnetic Field Theory Without Divergence Problems 2, A Least Invasively Quantized Theory, Journal of Statistical Physics, Volume 116, Issue 1, pp 1123-1159, 2004. M. Kiessling: On the motion of point defects in relativistic fields, in Quantum Field Theory and Gravity, Conceptual and Mathematical Advances in the Search for a Unified Framework, Finster e.a. (ed.), Springer, 2012. Y. Brenier: Some Geometric PDEs Related to Hydrodynamics and Electrodynamics, ICM Vol. III pp 761--772, 2002.

This episode discusses the Born-Infeld model for Electromagnetodynamics. Here, the standard model are the Maxwell equations coupling the interaction of magnetic and electric field with the help of a system of partial differential equations. This is a well-understood classical system. But in this classical model, one serious drawback is that the action of a point charge (which is represented by a Dirac measure on the right-hand side) leads to an infinite energy in the electric field which physically makes no sense. On the other hand, it should be possible to study the electric field of point charges since this is how the electric field is created. One solution for this challenge is to slightly change the point of view in a way similar to special relativity theory of Einstein. There, instead of taking the momentum () as preserved quantity and Lagrange parameter the Lagrangian is changed in a way that the bound for the velocity (in relativity the speed of light) is incorporated in the model. In the electromagnetic model, the Lagrangian would have to restrict the intensity of the fields. This was the idea which Borne and Infeld published already at the beginning of the last century. For the resulting system it is straightforward to calculate the fields for point charges. But unfortunately it is impossible to add the fields for several point charges (no superposition principle) since the resulting theory (and the PDE) are nonlinear. Physically this expresses, that the point charges do not act independently from each other but it accounts for certain interaction between the charges. Probably this interaction is really only important if charges are near enough to each other and locally it should be only influenced by the charge nearest. But it has not been possible to prove that up to now. The electrostatic case is elliptic but has a singularity at each point charge. So no classical regularity results are directly applicable. On the other hand, there is an interesting interplay with geometry since the PDE occurs as the mean curvature equation of hypersurfaces in the Minkowski space in relativity. The evolution problem is completely open. In the static case we have existence and uniqueness without really looking at the PDEs from the way the system is built. The PDE should provide at least qualitative information on the electric field. So if, e.g., there is a positive charge there could be a maximum of the field (for negative charges a minimum - respectively), and we would expect the field to be smooth outside these singular points. So a Lipschitz regular solution would seem probable. But it is open how to prove this mathematically. A special property is that the model has infinitely many inherent scales, namely all even powers of the gradient of the field. So to understand maybe asymptotic limits in theses scales could be a first interesting step. Denis Bonheure got his mathematical education at the Free University of Brussels and is working there as Professor of Mathematics at the moment. Literature and additional material M. Kiessling: Electromagnetic Field Theory Without Divergence Problems 1, The Born Legacy, Journal of Statistical Physics, Volume 116, Issue 1, pp 1057-1122, 2004. M. Kiessling: Electromagnetic Field Theory Without Divergence Problems 2, A Least Invasively Quantized Theory, Journal of Statistical Physics, Volume 116, Issue 1, pp 1123-1159, 2004. M. Kiessling: On the motion of point defects in relativistic fields, in Quantum Field Theory and Gravity, Conceptual and Mathematical Advances in the Search for a Unified Framework, Finster e.a. (ed.), Springer, 2012. Y. Brenier: Some Geometric PDEs Related to Hydrodynamics and Electrodynamics, ICM Vol. III pp 761--772, 2002.

Wed, 1 Jan 2014 12:00:00 +0100 https://epub.ub.uni-muenchen.de/25523/1/MA_Komboz.pdf Abou El-Komboz, Basil ddc:500, Ausgewählte Abschlussarbeiten, Statistik, Mathematik, Informatik un