@tante@tldr.nettime.orgThe "Turing Test" is not an actually relevant test for ... anything really.
Turing came up with a massively important theoretical concept (the Turing Machine). Helped with the Enigma machine. All impressive. "The Turing Test"? Not so much.
It's cute and interesting from a psychological and historical standpoint but that's it. It's not an actual metric.
@radioeinsmusicbot@mastodonapp.uk🇺🇦 Auf radioeins läuft...
Metric:
🎵 Help I'm Alive
#NowPlaying #Metric
https://knifes.bandcamp.com/track/metric-help-im-alive-knifes-remix
https://open.spotify.com/track/0cahtHEywK64NSWqm2SDTi
@Techmeme@techhub.socialAn analysis of Google TPU v6e vs AMD MI300X vs Nvidia H100/B200: Nvidia achieves a ~5x tokens-per-dollar advantage over TPU v6e and 2x advantage over MI300X (@artificialanlys)
https://x.com/artificialanlys/status/1993878037226557519
@BBC6MusicBot@mastodonapp.uk🇺🇦 #NowPlaying on #BBC6Music's #CraigCharles
Metric:
🎵 Victim of Luck
#Metric
#newRelease 🆕 single
https://open.spotify.com/track/5gH0Jr4nPOHPapmjfSYs4Y
@al3x@hachyderm.ioI have replaced the default browser on my iPhone. I sincerely hope this is one metric that Apple tracks and they’ll start realizing that Safari is not truly the better browser.
@kexpmusicbot@mastodonapp.uk🇺🇦 #NowPlaying on KEXP's #90TEEN
Metric:
🎵 Help I’m Alive
#Metric
https://knifes.bandcamp.com/track/metric-help-im-alive-knifes-remix
https://open.spotify.com/track/0cahtHEywK64NSWqm2SDTi
@cosmos4u@scicomm.xyzBored 'between the years'? Then help yourself to the papers "Primordial black holes within Higgs hybrid metric-Palatini approach", "The Serendipitous Axiodilaton: A Self-Consistent Recombination-Era Solution to the Hubble Tension" and "Ω1Ω2–ΛCDM: A promising phenomenological extension of the standard model of cosmology" all out today - #Universe at an elevated level ... ;-)
@Dragofix@veganism.socialUp to 4,700 metric tons of litter flows down the Rhine each year #Europe
@arXiv_condmatmtrlsci_bot@mastoxiv.pageFrom Berry curvature to quantum metric: a new era of quantum geometry metrology for Bloch electrons in solids
Bohm-Jung Yang
https://arxiv.org/abs/2512.24553 https://
@primonatura@mstdn.social"Up to 4,700 metric tons of litter flows down the Rhine each year"
#Rhine #Pollution #Litter
@Sustainable2050@mastodon.energyAnother year in which we've been making the climate crisis worse faster. And the role of aviation continues to grow nastier: probably good for 1/6 of the increase this year, caused by a small minority of the global population.
https://news.m…
@sean@scoat.esAmericans love fractions more than they hate the metric system.
(Just say 110 Golden Retrievers if you must. Or even 100. They don't all weigh the same anyway. The stupid here has layers.) https://mastodon.social/@Meyerweb/115945057468433055
@kexpmusicbot@mastodonapp.uk🇺🇦 #NowPlaying on KEXP's #VarietyMix
Metric:
🎵 Help I’m Alive
#Metric
https://knifes.bandcamp.com/track/metric-help-im-alive-knifes-remix
https://open.spotify.com/track/0cahtHEywK64NSWqm2SDTi
@cowboys@darktundra.xyzRanking 15 HoF Finalists by Career AV, do Witten, Woodson have a shot? https://cowboyswire.usatoday.com/story/sports/nfl/cowboys/2025/12/30/ranking-15-hof-finalists-by-career-av-do-witten-woodson-…
@UP8@mastodon.social🚧 Towards Modeling Road Access Deprivation in Sub-Saharan Africa Based on a New Accessibility Metric and Road Quality
#roads
@simon_brooke@mastodon.scot"This is the metric by which you can tell who in politics are your allies and who are your enemies: whether they support or oppose the extreme concentration of wealth. In fact, the matter should be definitional." — George Monbiot
#Kleptocracy
Money Talks – George Monbiot
@BBC6MusicBot@mastodonapp.uk @Dragofix@veganism.socialRecord fossil fuel emissions in 2025 despite renewables buildout, report says https://news.mongabay.com/short-article/2025/12/record-fossil-fuel-emissions-in-2025-despite-renewables-buildout-report-says/
@toxi@mastodon.thi.ngPrepping a digital negative of one of my old generative art projects (from 2008) for #Kallitype printing tomorrow. The form is actually _not_ 3D, but merely the time trace of a 2D physics sim of a single line (over hundreds of frames) and using spatial velocity deltas as metric for creating faux shading...
@paulbusch@mstdn.caGood Morning #Canada
I'm up early, cooking breakfast and got an 80s playlist on in the kitchen. What was happening in Canada in 1983...
- The metric system of weights and measures is officially adopted by the federal government
- Saskatchewan MLA Colin Thatcher resigns as Minister of Energy and Mines and a week later murders his wife, Joann
- Population of Canada hits 25M in November
- Steve Podborski wins Gold at the World Cup of Skiing
- Pierre Trudeau is PM
- Pay television begins operating in Canada
- Bill 101, protecting the French language in Quebec is ruled unconstitutional
- Brian Mulroney replaces Joe Clark as leader of Progressive Conservative Party of Canada
- Gas costs 47 cents/litre
- BC Place in Vancouver opens
- Air Canada flight 143 makes an emergency landing in Gimli, Manitoba
- Jeanne Sauvé is appointed Canada's first female Governor General
- Average house price is $74,500, 5-yr mortgage rate was 13.5%
#CanadaIsAwesome #History #CanadaFlashback
https://youtu.be/IPznPZLNQhI
@grumpybozo@toad.socialRE: https://lgbtqia.space/@dianea/115944820180442960
It’s not about the metric system.
We largely do not know our own basic units well.
For the lurkers: 100mm=10cm~4in.= pack of "100" size cigarettes. Those don’t change size like the S…
@mxp@mastodon.acm.orgI rarely make electronic shopping lists, so I only discovered today that the Notes app has a handy feature that converts kilograms into tons. Even when using the comma as decimal separator! It doesn’t recognize “dl” (customary in Switzerland), though, and come to think of it, it has none of the features demoed by Doug Engelbart in 1968.
@Mediagazer@mstdn.socialNetflix rolls out a new ad metric called monthly active viewers, or MAV, and says it has 190M such viewers in the 12 countries where it offers an ad tier (Rick Porter/The Hollywood Reporter)
https://www.hollywoodreporter.com/business
@radioeinsmusicbot@mastodonapp.uk🇺🇦 Auf radioeins läuft...
Metric:
🎵 Lie Lie Lie
#NowPlaying #Metric
https://metriccheesehead.bandcamp.com/track/all-a-lie-02
@arXiv_mathDG_bot@mastoxiv.pageReplaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Weighted GJMS operators on smooth metric measure spaces
Ayush Khaitan
https:/…
@ripienaar@devco.socialBeen giving Home Assistant another try. It’s ok I guess.
Probsbly not a common problem but there really is no good solutions that I could find for managing multiple locations from a single instance or even some kind of federated view or something.
Integrating Choria Switch and Metric abstractions into it So I can pull in sensor stats and interact with heaters etc - but let Choria keep autonomously own the devices.
(Also a updated picture of my Pi case for sensors)
@brichapman@mastodon.socialMassachusetts is about to see major savings from clean energy. A new analysis shows the state's SMART 3.0 solar-plus-storage program could save ratepayers $313 million annually by 2030.
The key? Pushing out inefficient natural gas plants, cutting reliance on fossil fuels during winter, and slashing 1.6 million metric tons of CO2 per year.
@fortune@social.linux.pizzaBOFH excuse #242:
Software uses US measurements, but the OS is in metric...
@Techmeme@techhub.socialNetflix rolls out a new ad metric called monthly active viewers, or MAV, and says it has 190M such viewers in the 12 countries where it offers an ad tier (Rick Porter/The Hollywood Reporter)
https://www.hollywoodreporter.com/business
@brewsterkahle@mastodon.archive.org$0.50 per mile for electricity for a semi truck? wow, lower than I would imagine. (and it can be as low as $0.12 where rates are lower.).
"During testing, the truck averaged 1.72 kWh per mile while hauling a gross combined weight of 75,000 pounds (34 metric tons) over a 390-mile (625 km) long-haul route."
a tesla model 3 is ~0.3 kWh per mile.
@timjan@social.linux.pizza"I'm only finding metric adjustable wrenches. Where are the customary sized?"
@sjn@chaos.social @UP8@mastodon.social🎗️ North Sea project promises to return carbon to exactly where it came from
https://www.japantimes.co.jp/environment/2025/12/22/climate-change/co2-denmark-north-sea/
🆓
@arXiv_csGT_bot@mastoxiv.pageInvariant Price of Anarchy: a Metric for Welfarist Traffic Control
Ilia Shilov, Mingjia He, Heinrich H. Nax, Emilio Frazzoli, Gioele Zardini, Saverio Bolognani
https://arxiv.org/abs/2512.05843 https://arxiv.org/pdf/2512.05843 https://arxiv.org/html/2512.05843
arXiv:2512.05843v1 Announce Type: new
Abstract: The Price of Anarchy (PoA) is a standard metric for quantifying inefficiency in socio-technical systems, widely used to guide policies like traffic tolling. Conventional PoA analysis relies on exact numerical costs. However, in many settings, costs represent agents' preferences and may be defined only up to possibly arbitrary scaling and shifting, representing informational and modeling ambiguities. We observe that while such transformations preserve equilibrium and optimal outcomes, they change the PoA value. To resolve this issue, we rely on results from Social Choice Theory and define the Invariant PoA. By connecting admissible transformations to degrees of comparability of agents' costs, we derive the specific social welfare functions which ensure that efficiency evaluations do not depend on arbitrary rescalings or translations of individual costs. Case studies on a toy example and the Zurich network demonstrate that identical tolling strategies can lead to substantially different efficiency estimates depending on the assumed comparability. Our framework thus demonstrates that explicit axiomatic foundations are necessary in order to define efficiency metrics and to appropriately guide policy in large-scale infrastructure design robustly and effectively.
toXiv_bot_toot
@JSkier@social.linux.pizzaDang, it's cold (-18 C overnight low for all you metric peeps). No #running outside lately. I intend to run on an indoor track during the week this week.
@jlpiraux@wallonie-bruxelles.socialLa pollution plastique va plus que doubler d'ici 2040, générant l'équivalent d'un camion poubelle de déchets chaque seconde.
#plastique #environnement
@Techmeme@techhub.socialApple details how it is 3D printing Watch Series 11 and Ultra 3 cases using titanium powder, helping Apple save 400 metric tons of raw titanium in 2025 (Apple)
https://www.apple.com/newsroom/2025/11/mapping-the-future-with-3d-printed-tita…
@brichapman@mastodon.socialFive New England states just launched a $450M initiative to make heat pumps way more accessible.
The plan? Incentivize contractors to keep units in stock, dropping upfront costs by $500-$700 per heat pump. The goal is 580,000 residential installations by 2030, cutting 2.5M metric tons of carbon while lowering energy bills.
@jamesthebard@social.linux.pizzaI stayed up far too long tonight for this one, but it was fun. Saw that we were dealing with an absolute metric ton of ranges at the very beginning so my initial thought was to reduce/merge those ranges and that's what I spent most of my time on before even tackling part 1.
It paid off tremendously and made solving everything very, very easy. There's still the Nim version to write, but I'll handle that after I get some sleep.
Solution:
@kexpmusicbot@mastodonapp.uk
@arXiv_csLG_bot@mastoxiv.pageReplaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[1/5]:
- Feed Two Birds with One Scone: Exploiting Wild Data for Both Out-of-Distribution Generalization a...
Haoyue Bai, Gregory Canal, Xuefeng Du, Jeongyeol Kwon, Robert Nowak, Yixuan Li
https://arxiv.org/abs/2306.09158
- Sparse, Efficient and Explainable Data Attribution with DualXDA
Galip \"Umit Yolcu, Moritz Weckbecker, Thomas Wiegand, Wojciech Samek, Sebastian Lapuschkin
https://arxiv.org/abs/2402.12118 https://mastoxiv.page/@arXiv_csLG_bot/111962593972369958
- HGQ: High Granularity Quantization for Real-time Neural Networks on FPGAs
Sun, Que, {\AA}rrestad, Loncar, Ngadiuba, Luk, Spiropulu
https://arxiv.org/abs/2405.00645 https://mastoxiv.page/@arXiv_csLG_bot/112370274737558603
- On the Identification of Temporally Causal Representation with Instantaneous Dependence
Li, Shen, Zheng, Cai, Song, Gong, Chen, Zhang
https://arxiv.org/abs/2405.15325 https://mastoxiv.page/@arXiv_csLG_bot/112511890051553111
- Basis Selection: Low-Rank Decomposition of Pretrained Large Language Models for Target Applications
Yang Li, Daniel Agyei Asante, Changsheng Zhao, Ernie Chang, Yangyang Shi, Vikas Chandra
https://arxiv.org/abs/2405.15877 https://mastoxiv.page/@arXiv_csLG_bot/112517547424098076
- Privacy Bias in Language Models: A Contextual Integrity-based Auditing Metric
Yan Shvartzshnaider, Vasisht Duddu
https://arxiv.org/abs/2409.03735 https://mastoxiv.page/@arXiv_csLG_bot/113089789682783135
- Low-Rank Filtering and Smoothing for Sequential Deep Learning
Joanna Sliwa, Frank Schneider, Nathanael Bosch, Agustinus Kristiadi, Philipp Hennig
https://arxiv.org/abs/2410.06800 https://mastoxiv.page/@arXiv_csLG_bot/113283021321510736
- Hierarchical Multimodal LLMs with Semantic Space Alignment for Enhanced Time Series Classification
Xiaoyu Tao, Tingyue Pan, Mingyue Cheng, Yucong Luo, Qi Liu, Enhong Chen
https://arxiv.org/abs/2410.18686 https://mastoxiv.page/@arXiv_csLG_bot/113367101100828901
- Fairness via Independence: A (Conditional) Distance Covariance Framework
Ruifan Huang, Haixia Liu
https://arxiv.org/abs/2412.00720 https://mastoxiv.page/@arXiv_csLG_bot/113587817648503815
- Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning
Simon Frieder, et al.
https://arxiv.org/abs/2412.15184 https://mastoxiv.page/@arXiv_csLG_bot/113683924322164777
- Pairwise Elimination with Instance-Dependent Guarantees for Bandits with Cost Subsidy
Ishank Juneja, Carlee Joe-Wong, Osman Ya\u{g}an
https://arxiv.org/abs/2501.10290 https://mastoxiv.page/@arXiv_csLG_bot/113859392622871057
- Towards Human-Guided, Data-Centric LLM Co-Pilots
Evgeny Saveliev, Jiashuo Liu, Nabeel Seedat, Anders Boyd, Mihaela van der Schaar
https://arxiv.org/abs/2501.10321 https://mastoxiv.page/@arXiv_csLG_bot/113859392688054204
- Regularized Langevin Dynamics for Combinatorial Optimization
Shengyu Feng, Yiming Yang
https://arxiv.org/abs/2502.00277
- Generating Samples to Probe Trained Models
Eren Mehmet K{\i}ral, Nur\c{s}en Ayd{\i}n, \c{S}. \.Ilker Birbil
https://arxiv.org/abs/2502.06658 https://mastoxiv.page/@arXiv_csLG_bot/113984059089245671
- On Agnostic PAC Learning in the Small Error Regime
Julian Asilis, Mikael M{\o}ller H{\o}gsgaard, Grigoris Velegkas
https://arxiv.org/abs/2502.09496 https://mastoxiv.page/@arXiv_csLG_bot/114000974082372598
- Preconditioned Inexact Stochastic ADMM for Deep Model
Shenglong Zhou, Ouya Wang, Ziyan Luo, Yongxu Zhu, Geoffrey Ye Li
https://arxiv.org/abs/2502.10784 https://mastoxiv.page/@arXiv_csLG_bot/114023667639951005
- On the Effect of Sampling Diversity in Scaling LLM Inference
Wang, Liu, Chen, Light, Liu, Chen, Zhang, Cheng
https://arxiv.org/abs/2502.11027 https://mastoxiv.page/@arXiv_csLG_bot/114023688225233656
- How to use score-based diffusion in earth system science: A satellite nowcasting example
Randy J. Chase, Katherine Haynes, Lander Ver Hoef, Imme Ebert-Uphoff
https://arxiv.org/abs/2505.10432 https://mastoxiv.page/@arXiv_csLG_bot/114516300594057680
- PEAR: Equal Area Weather Forecasting on the Sphere
Hampus Linander, Christoffer Petersson, Daniel Persson, Jan E. Gerken
https://arxiv.org/abs/2505.17720 https://mastoxiv.page/@arXiv_csLG_bot/114572963019603744
- Train Sparse Autoencoders Efficiently by Utilizing Features Correlation
Vadim Kurochkin, Yaroslav Aksenov, Daniil Laptev, Daniil Gavrilov, Nikita Balagansky
https://arxiv.org/abs/2505.22255 https://mastoxiv.page/@arXiv_csLG_bot/114589956040892075
- A Certified Unlearning Approach without Access to Source Data
Umit Yigit Basaran, Sk Miraj Ahmed, Amit Roy-Chowdhury, Basak Guler
https://arxiv.org/abs/2506.06486 https://mastoxiv.page/@arXiv_csLG_bot/114658421178857085
toXiv_bot_toot
@arXiv_csGR_bot@mastoxiv.pageProc3D: Procedural 3D Generation and Parametric Editing of 3D Shapes with Large Language Models
Fadlullah Raji, Stefano Petrangeli, Matheus Gadelha, Yu Shen, Uttaran Bhattacharya, Gang Wu
https://arxiv.org/abs/2601.12234 https://arxiv.org/pdf/2601.12234 https://arxiv.org/html/2601.12234
arXiv:2601.12234v1 Announce Type: new
Abstract: Generating 3D models has traditionally been a complex task requiring specialized expertise. While recent advances in generative AI have sought to automate this process, existing methods produce non-editable representation, such as meshes or point clouds, limiting their adaptability for iterative design. In this paper, we introduce Proc3D, a system designed to generate editable 3D models while enabling real-time modifications. At its core, Proc3D introduces procedural compact graph (PCG), a graph representation of 3D models, that encodes the algorithmic rules and structures necessary for generating the model. This representation exposes key parameters, allowing intuitive manual adjustments via sliders and checkboxes, as well as real-time, automated modifications through natural language prompts using Large Language Models (LLMs). We demonstrate Proc3D's capabilities using two generative approaches: GPT-4o with in-context learning (ICL) and a fine-tuned LLAMA-3 model. Experimental results show that Proc3D outperforms existing methods in editing efficiency, achieving more than 400x speedup over conventional approaches that require full regeneration for each modification. Additionally, Proc3D improves ULIP scores by 28%, a metric that evaluates the alignment between generated 3D models and text prompts. By enabling text-aligned 3D model generation along with precise, real-time parametric edits, Proc3D facilitates highly accurate text-based image editing applications.
toXiv_bot_toot
@arXiv_mathOC_bot@mastoxiv.pageMeasuring dissimilarity between convex cones by means of max-min angles
Welington de Oliveira, Valentina Sessa, David Sossa
https://arxiv.org/abs/2511.10483 https://arxiv.org/pdf/2511.10483 https://arxiv.org/html/2511.10483
arXiv:2511.10483v1 Announce Type: new
Abstract: This work introduces a novel dissimilarity measure between two convex cones, based on the max-min angle between them. We demonstrate that this measure is closely related to the Pompeiu-Hausdorff distance, a well-established metric for comparing compact sets. Furthermore, we examine cone configurations where the measure admits simplified or analytic forms. For the specific case of polyhedral cones, a nonconvex cutting-plane method is deployed to compute, at least approximately, the measure between them. Our approach builds on a tailored version of Kelley's cutting-plane algorithm, which involves solving a challenging master program per iteration. When this master program is solved locally, our method yields an angle that satisfies certain necessary optimality conditions of the underlying nonconvex optimization problem yielding the dissimilarity measure between the cones. As an application of the proposed mathematical and algorithmic framework, we address the image-set classification task under limited data conditions, a task that falls within the scope of the \emph{Few-Shot Learning} paradigm. In this context, image sets belonging to the same class are modeled as polyhedral cones, and our dissimilarity measure proves useful for understanding whether two image sets belong to the same class.
toXiv_bot_toot
@arXiv_physicsgenph_bot@mastoxiv.pageGeometric Interpretation of the Redshift Evolution of H_0(z)
Seokcheon Lee
https://arxiv.org/abs/2511.07454 https://arxiv.org/pdf/2511.07454 https://arxiv.org/html/2511.07454
arXiv:2511.07454v1 Announce Type: new
Abstract: Recent analyses of the Master Type Ia supernova (SN Ia) sample have revealed a mild redshift dependence in the inferred local Hubble parameter, often expressed as tilde{H}_0(z) = H_0 (1 z)^{-\alpha}, where \alpha quantifies possible departures from the standard cosmological time dilation relation. In this work, we show that such an empirical scaling can be interpreted as a purely geometric effect arising from a small, gauge-dependent normalization of cosmic time within the Robertson-Walker metric. This interpretation naturally unifies the observed redshift evolution of tilde{H}_0(z) and the corresponding deviation in SN Ia light-curve durations under a single geometric time-normalization framework. We demonstrate that this mapping leaves all background distances--linked to the Hubble radius in the general-relativistic frame--unchanged, while the apparent evolution in SN Ia luminosity distances arises from the redshift dependence of the Chandrasekhar mass. The result provides a unified and observationally consistent explanation of the mild Hubble-tension trend as a manifestation of the geometric structure of cosmic time rather than a modification of the expansion dynamics.
toXiv_bot_toot
@Techmeme@techhub.social1Password CEO David Faugno says the company has crossed $400M in ARR, up from $250M in 2023, as it benefits from a shift in the threat landscape due to AI (Samantha Subin/CNBC)
https://www.cnbc.com/2025/11/06/ryan-reynolds-backed-1password-tops-400…
@UP8@mastodon.social📉 Eating more but growing less: Stagnant Philippine farms linked to widening rice gap
#food
@kexpmusicbot@mastodonapp.uk🇺🇦 #NowPlaying on #KEXP's #VarietyMix
Metric:
🎵 Help I’m Alive (acoustic)
#Metric
https://knifes.bandcamp.com/track/metric-help-im-alive-knifes-remix
https://open.spotify.com/track/0cahtHEywK64NSWqm2SDTi
@arXiv_mathOC_bot@mastoxiv.pageVerification of Sequential Convex Programming for Parametric Non-convex Optimization
Rajiv Sambharya, Nikolai Matni, George Pappas
https://arxiv.org/abs/2511.10622 https://arxiv.org/pdf/2511.10622 https://arxiv.org/html/2511.10622
arXiv:2511.10622v1 Announce Type: new
Abstract: We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem that maximizes a performance metric (e.g., the suboptimality after a given number of iterations) over parameters constrained to be in a parameter set and iterate sequences consistent with the SCP update rules. Our framework is general, extending the notion of SCP to include both conventional variants such as trust-region, convex-concave, and prox-linear methods, and algorithms that combine convex subproblems with rounding steps, as in relaxing and rounding schemes. Unlike existing analyses that may only provide local guarantees under limited conditions, our framework delivers global worst-case guarantees--quantifying how well an SCP algorithm performs across all problem instances in the specified family. Applications in control, signal processing, and operations research demonstrate that our framework provides, for the first time, global worst-case guarantees for SCP algorithms in the parametric setting.
toXiv_bot_toot
@UP8@mastodon.social📉 COP30: Zimbabwe's forest and energy projects reveal the downside of carbon credits
#zimbabwe
@arXiv_mathOC_bot@mastoxiv.pageTime-periodic branched transport
Jun Kitagawa, Cecilia Mikat
https://arxiv.org/abs/2511.10498 https://arxiv.org/pdf/2511.10498 https://arxiv.org/html/2511.10498
arXiv:2511.10498v1 Announce Type: new
Abstract: We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but the source and target mass distributions can change cyclically over time, such as road networks or circulatory systems. We introduce the notion of time-dependent transport paths along with associated energies and distances, and prove existence of transport paths whose energy achieves the distance. We also show the time-dependent transport yields a metric structure on subsets of appropriately defined measure-valued Sobolev spaces.
toXiv_bot_toot
@arXiv_mathOC_bot@mastoxiv.pageThe Age-Structured Chemostat with Substrate Dynamics as a Control System
Iasson Karafyllis, Dionysis Theodosis, Miroslav Krstic
https://arxiv.org/abs/2511.09963 https://arxiv.org/pdf/2511.09963 https://arxiv.org/html/2511.09963
arXiv:2511.09963v1 Announce Type: new
Abstract: In this work we study an age-structured chemostat model with a renewal boundary condition and a coupled substrate equation. The model is nonlinear and consists of a hyperbolic partial differential equation and an ordinary differential equation with nonlinear, nonlocal terms appearing both in the ordinary differential equation and the boundary condition. Both differential equations contain a non-negative control input, while the states of the model are required to be positive. Under an appropriate weak solution framework, we determine the state space and the input space for this model. We prove global existence and uniqueness of solutions for all admissible initial conditions and all allowable control inputs. To this purpose we employ a combination of Banach's fixed-point theorem with implicit solution formulas and useful solution estimates. Finally, we show that the age-structured chemostat model gives a well-defined control system on a metric space.
toXiv_bot_toot
