arXiv subjects

Miguel Martin

Publications and source records attributed to Miguel Martin.

At least 19 recordsLinked to original sources

arXiv2026

The Bishop-Phelps-Bollob\'as property for the numerical radius: a Zizler-type approach

We investigate the Bishop-Phelps-Bollob\'as property for the numerical radius (BPBp-nu) through a Zizler-type perspective on the classical Bishop-Phelps-Bollob\'as property (BPBp). This approach allows us to establish two new results: the real Banach space $\ell_\infty$ satisfies the BPBp-nu, while the complex space $\ell_1 \oplus_\infty c_0$ does not. Note that the latter provides the first natural example (constructed without renorming techniques) of a Banach space where the numerical radius attaining operators are dense but the BPBp-nu fails. Along the way, we strengthen the main results of the paper [Kim et al, On the Bishop-Phelps-Bollob\'as theorem for operators and numerical radius, Studia Math., 2016] concerning the interplay between the BPBp for the pair $(X,Y)$ and the BPBp-nu for a direct sum $X\oplus Y$ of Banach spaces. We further explore the validity of the Zizler-type BPBp across different pairs of Banach spaces, and how this property relates to the classical BPBp and the BPBp-nu. Finally, we specialize our analysis to the framework of compact operators.

math.FA↗

arXiv2025

Scalable and Performant Data Loading

We present SPDL (Scalable and Performant Data Loading), an open-source, framework-agnostic library designed for efficiently loading array data to GPU. Data loading is often a bottleneck in AI applications, and is challenging to optimize because it requires coordination of network calls, CPU-bound tasks, and GPU device transfer. On top of that, Python's GIL (Global Interpreter Lock) makes it difficult to gain performance improvement from multi-threading. We found that when data preprocessing functions release the GIL entirely, it is possible to execute them concurrently in a thread pool, thereby improving the workflow performance. Our benchmark shows that compared to the PyTorch DataLoader, SPDL can iterate through the ImageNet dataset 74% faster while using 38% less CPU and 50GB less memory. When training ViT-B/16 model, SPDL can send data to the GPU at a speed that does not starve the training. Additionally, when using SPDL on Python 3.13t, without changing any code, the throughput is further by improved by 33%, thanks to the disabled GIL. SPDL can improve the performance of current AI model training, and receives further performance improvements when Free-Threaded Python is adopted in production systems. SPDL is available at https://github.com/facebookresearch/spdl.

cs.DC↗

arXiv2025

PerceptionLM: Open-Access Data and Models for Detailed Visual Understanding

Vision-language models are integral to computer vision research, yet many high-performing models remain closed-source, obscuring their data, design and training recipe. The research community has responded by using distillation from black-box models to label training data, achieving strong benchmark results, at the cost of measurable scientific progress. However, without knowing the details of the teacher model and its data sources, scientific progress remains difficult to measure. In this paper, we study building a Perception Language Model (PLM) in a fully open and reproducible framework for transparent research in image and video understanding. We analyze standard training pipelines without distillation from proprietary models and explore large-scale synthetic data to identify critical data gaps, particularly in detailed video understanding. To bridge these gaps, we release 2.8M human-labeled instances of fine-grained video question-answer pairs and spatio-temporally grounded video captions. Additionally, we introduce PLM-VideoBench, a suite for evaluating challenging video understanding tasks focusing on the ability to reason about "what", "where", "when", and "how" of a video. We make our work fully reproducible by providing data, training recipes, code & models. https://github.com/facebookresearch/perception_models

cs.CV↗

arXiv2024

A Banach space whose set of norm-attaining functionals is algebraically trivial

We construct a Banach space $X$ for which the set of norm-attaining functionals $NA(X,\mathbb{R})$ does not contain any non-trivial cone. Even more, given two linearly independent norm-attaining functionals on $X$, no other element of the segment between them attains its norm. Equivalently, the intersection of $NA(X,\mathbb{R})$ with a two-dimensional subspace of $X^*$ is contained in the union of two lines. In terms of proximinality, we show that for every closed subspace $M$ of $X$ of codimension two, at most four elements of the unit sphere of $X/M$ have a representative of norm-one. We further relate this example with an open problem on norm-attaining operators.

math.FA↗

arXiv2024

InfraRed Investigation in Singapore (IRIS) Observatory: Urban heat island contributors and mitigators analysis using neighborhood-scale thermal imaging

This paper studies heat fluxes from contributors and mitigators of urban heat islands using thermal images and weather data. Thermal images were collected from an observatory operating on the rooftop of a building between November 2021 and April 2022. Over the same period, an automatic weather station network was used to measure weather conditions at several locations on a university campus in Singapore. From data collected by the observatory and the automatic weather station network, a method was developed to estimate the heat emitted by building facades, vegetation, and traffic. Before performing the analysis of urban heat fluxes, it was observed that the surface temperature collected from the observatory is sensitive to some variables. After the sensitivity analysis, thermal images were calibrated against measurements of the surface temperature in an outdoor environment. Finally, several contributors and mitigators of urban heat islands were analyzed from heat fluxes assessed with thermal images and weather data. According to thermal images collected by the rooftop observatory, concrete walls are an important contributor to urban heat islands due to the longwave radiation they emit at night. Vegetation, on the other hand, seems to be an effective mitigator because of latent heat fluxes generated by evapotranspiration. Traffic looks to be a negligible source of heat if considered over a small portion of a road. In the future, more efforts can be made to estimate the magnitude of the heat released by an air-conditioning system from thermal images.

physics.ao-ph↗

arXiv2024

A numerical range approach to Birkhoff-James orthogonality with applications

The main aim of this paper is to provide characterizations of Birkhoff-James orthogonality (BJ-orthogonality in short) in a number of families of Banach spaces in terms of the elements of significant subsets of the unit ball of their dual spaces, which makes the characterizations more applicable. The tool to do so is a fine study of the abstract numerical range and its relation with the BJ-orthogonality. Among other results, we provide a characterization of BJ-orthogonality for spaces of vector-valued bounded functions in terms of the domain set and the dual of the target space, which is applied to get results for spaces of vector-valued continuous functions, uniform algebras, Lipschitz maps, injective tensor products, bounded linear operators with respect to the operator norm and to the numerical radius, multilinear maps, and polynomials. Next, we study possible extensions of the well-known Bhatia-Šemrl theorem on BJ-orthogonality of matrices, showing results in spaces of vector-valued continuous functions, compact linear operators on reflexive spaces, and finite Blaschke products. Finally, we find applications of our results to the study of spear vectors and spear operators. We show that no smooth point of a Banach space can be BJ-orthogonal to a spear vector of $Z$. As a consequence, if $X$ is a Banach space containing strongly exposed points and $Y$ is a smooth Banach space with dimension at least two, then there are no spear operators from $X$ to $Y$. Particularizing this result to the identity operator, we show that a smooth Banach space containing strongly exposed points has numerical index strictly smaller than one. These latter results partially solve some open problems.

math.FA↗

arXiv2024

Slicely countably determined points in Banach spaces

We introduce slicely countably determined points (SCD points) of a bounded and convex subset of a Banach space which extends the notions of denting points, strongly regular points and much more. We completely characterize SCD points in the unit balls of $L_1$-preduals. We study SCD points in direct sums of Banach spaces and obtain that an infinite sum of Banach spaces may have an SCD point despite the fact that none of its components have it. We then prove sufficient conditions to get that an elementary tensor $x\otimes y$ is an SCD point in the unit ball of the projective tensor product $X \widehat{\otimes}_πY$. Regarding Lipschitz-free spaces on compact metric spaces, we show that norm one SCD points of their unit balls are exactly the ones that can be approximated by convex combinations of strongly exposed points of the unit ball. Finally, as applications, we prove a new inheritance result for the Daugavet property to its subspaces, we show that separable Banach spaces for which every convex series of slices intersects the unit sphere must contain an isomorphic copy of $\ell_1$, and we get pointwise conditions on an operator on a Banach space with the Daugavet property to satisfy the Daugavet equation.

math.FA↗

arXiv2023

District-scale surface temperatures generated from high-resolution longitudinal thermal infrared images

The paper describes a dataset that was collected by infrared thermography, which is a non-contact, non-intrusive technique to collect data and analyze the built environment in various aspects. While most studies focus on the city and building scales, the rooftop observatory provides high temporal and spatial resolution observations with dynamic interactions on the district scale. The rooftop infrared thermography observatory with a multi-modal platform that is capable of assessing a wide range of dynamic processes in urban systems was deployed in Singapore. It was placed on the top of two buildings that overlook the outdoor context of the campus of the National University of Singapore. The platform collects remote sensing data from tropical areas on a temporal scale, allowing users to determine the temperature trend of individual features such as buildings, roads, and vegetation. The dataset includes 1,365,921 thermal images collected on average at approximately 10 seconds intervals from two locations during ten months.

cs.CV↗

arXiv2023

Ego-Exo4D: Understanding Skilled Human Activity from First- and Third-Person Perspectives

We present Ego-Exo4D, a diverse, large-scale multimodal multiview video dataset and benchmark challenge. Ego-Exo4D centers around simultaneously-captured egocentric and exocentric video of skilled human activities (e.g., sports, music, dance, bike repair). 740 participants from 13 cities worldwide performed these activities in 123 different natural scene contexts, yielding long-form captures from 1 to 42 minutes each and 1,286 hours of video combined. The multimodal nature of the dataset is unprecedented: the video is accompanied by multichannel audio, eye gaze, 3D point clouds, camera poses, IMU, and multiple paired language descriptions -- including a novel "expert commentary" done by coaches and teachers and tailored to the skilled-activity domain. To push the frontier of first-person video understanding of skilled human activity, we also present a suite of benchmark tasks and their annotations, including fine-grained activity understanding, proficiency estimation, cross-view translation, and 3D hand/body pose. All resources are open sourced to fuel new research in the community. Project page: http://ego-exo4d-data.org/

cs.CV↗

arXiv2023

Generating operators between Banach spaces

We introduce and study the notion of generating operators as those norm-one operators $G\colon X\longrightarrow Y$ such that for every $0<δ<1$, the set $\{x\in X\colon \|x\|\leq 1,\ \|Gx\|>1-δ\}$ generates the unit ball of $X$ by closed convex hull. This class of operators includes isometric embeddings, spear operators (actually, operators with the alternative Daugavet property), and other examples like the natural inclusions of $\ell_1$ into $c_0$ and of $L_\infty[0,1]$ into $L_1[0,1]$. We first present a characterization in terms of the adjoint operator, make a discussion on the behaviour of diagonal generating operators on $c_0$-, $\ell_1$-, and $\ell_\infty$-sums, and present examples in some classical Banach spaces. Even though rank-one generating operators always attain their norm, there are generating operators, even of rank-two, which do not attain their norm. We discuss when a Banach space can be the domain of a generating operator which does not attain its norm in terms of the behaviour of some spear sets of the dual space. Finally, we study when the set of all generating operators between two Banach spaces $X$ and $Y$ generates all non-expansive operators by closed convex hull. We show that this is the case when $X=L_1(μ)$ and $Y$ has the Radon-Nikodým property with respect to $μ$. Therefore, when $X=\ell_1(Γ)$, this is the case for every target space $Y$. Conversely, we also show that a real finite-dimensional space $X$ satisfies that generating operators from $X$ to $Y$ generate all non-expansive operators by closed convex hull only in the case that $X$ is an $\ell_1$-space.

math.FA↗

arXiv2023

Longitudinal thermal imaging for scalable non-residential HVAC and occupant behaviour characterization

This work presents a study on the characterization of the air-conditioning (AC) usage pattern of non-residential buildings from thermal images collected from an urban-scale infrared (IR) observatory. To achieve this first, an image processing scheme, for cleaning and extraction of the temperature time series from the thermal images is implemented. To test the accuracy of the thermal measurements using IR camera, the extracted temperature is compared against the ground truth surface temperature measurements. It is observed that the detrended thermal measurements match well with the ground truth surface temperature measurements. Subsequently, the operational pattern of the water-cooled systems and window AC units are extracted from the analysis of the thermal signature. It is observed that for the water-cooled system, the difference between the rate of change of the window and wall can be used to extract the operational pattern. While, in the case of the window AC units, wavelet transform of the AC unit temperature is used to extract the frequency and time domain information of the AC unit operation. The results of the analysis are compared against the indoor temperature sensors installed in the office spaces of the building. It is realized that the accuracy in the prediction of the operational pattern is highest between 8 pm to 10 am, and it reduces during the day because of solar radiation and high daytime temperature. Subsequently, a characterization study is conducted for eight window/split AC units from the thermal image collected during the nighttime. This forms one of the first studies on the operational behavior of HVAC systems for non-residential buildings using the longitudinal thermal imaging technique. The output from this study can be used to better understand the operational and occupant behavior, without requiring to deploy a large array of sensors in the building space.

cs.CV↗

arXiv2023

Diametral notions for elements of the unit ball of a Banach space

We introduce extensions of $Δ$-points and Daugavet points in which slices are replaced by relative weakly open subsets (super $Δ$-points and super Daugavet points) or by convex combinations of slices (ccs $Δ$-points and ccs Daugavet points). We first give a general overview on these new concepts and provide some isometric consequences on the spaces. As examples: if a Banach space contains a super $Δ$-point, then it does not admit an unconditional FDD with suppression constant smaller than two; if a real Banach space contains a ccs $Δ$-point, then it does not admit a one-unconditional basis; if a Banach space contains a ccs Daugavet point, then every convex combination of slices of its unit ball has diameter two. We next characterize the notions in some classes of Banach spaces showing, for instance, that all the notions coincide in $L_1$-predual spaces and that all the notions but ccs Daugavet points coincide in $L_1$-spaces. We next remark on some examples which have previously appeared in the literature and provide some new intriguing examples: examples of super $Δ$-points which are as closed as desired to strongly exposed points (hence failing to be Daugavet points in an extreme way); an example of a super $Δ$-point which is strongly regular (hence failing to be a ccs $Δ$-point in the strongest way); a super Daugavet point which fails to be a ccs $Δ$-point. The extensions of the diametral notions to point in the open unit ball and the consequences on the spaces are also studied. Last, we investigate the Kuratowski measure of relative weakly open subsets and of convex combinations of slices in the presence of super $Δ$-points or ccs $Δ$-points, as well as for spaces enjoying diameter 2 properties. We conclude the paper with a section on open problems.

math.FA↗

arXiv2022

The AEROS ocean observation mission and its CubeSat pathfinder

AEROS aims to develop a nanosatellite as a precursor of a future system of systems, which will include assets and capabilities of both new and existing platforms operating in the Ocean and Space, equipped with state-of-the-art sensors and technologies, all connected through a communication network linked to a data gathering, processing and dissemination system. This constellation leverages scientific and economic synergies emerging from New Space and the opportunities in prospecting, monitoring, and valuing the Ocean in a sustainable manner, addressing the demand for improved spatial, temporal, and spectral coverage in areas such as coastal ecosystems management and climate change assessment and mitigation. Currently, novel sensors and systems, including a miniaturized hyperspectral imager and a flexible software-defined communication system, are being developed and integrated into a new versatile satellite structure, supported by an innovative on-board software. Additional sensors, like the LoRaWAN protocol and a wider field of view RGB camera, are under study. To cope with data needs, a Data Analysis Centre, including a cloud-based data and telemetry dashboard and a back-end layer, to receive and process acquired and ingested data, is being implemented to provide tailored-to-use remote sensing products for a wide range of applications for private and institutional stakeholders.

physics.ao-ph↗

arXiv2022

MAGAL Constellation -- Using a Small Satellite Altimeter Constellation to Monitor Local and Regional Ocean and Inland Water Variations

MAGAL lays the foundations for a future constellation of small satellites carrying radar altimeters aiming to improve the understanding of ocean circulation variability at local, regional, and global scales. All necessary tools will be developed, including a new small, low-power altimeter payload and a miniaturized satellite platform, grounded on the Space 4.0 industry, to be manufactured inseries, minimizing production, operational and launch costs. To implement a collaborative constellation, and better tackle the gaps of large radar altimeter programmes, MAGAL will use a Data Analysis Centre, based on cloud services, for storage and process of data, based on known and improved algorithms, including overlay of layers from multiple sources (e.g. meteorology and opensource data). As a constellation of six satellites, MAGAL increases the density of sea surface topography measurements, enabling more data for altimetry products, when used in synergy with other missions, in coastal areas and over mesoscale features. This results in scientific and commercial information aggregated into a single platform, displayed in various graphical interfaces, allowing overlaid correlations. MAGAL is aligned with the insights from the EU agenda for sustainable development, adding value, alongside the underlying technology development, bringing together the sea's economy and its sustainable growth.

physics.ao-ph↗

arXiv2022

AEROS: Oceanographic Hyperspectral Imaging and Argos-Tracking CubeSat

AEROS is a 3U CubeSat pathfinder toward a future ocean-observing constellation, targeting the Portuguese Atlantic region. AEROS features a miniaturized, high-resolution Hyperspectral Imager (HSI), a 5MP RGB camera, and a Software Defined Radio (SDR). The sensor generated data will be processed and aggregated for end-users in a new web-based Data Analysis Center (DAC). The HSI has 150 spectrally contiguous bands covering visible to near-infrared with 10 nm bandwidth. The HSI collects ocean color data to support studies of oceanographic characteristics known to influence the spatio-temporal distribution and movement behavior of marine organisms. Usage of an SDR expands AEROS's operational and communication range and allows for remote reconfiguration. The SDR receives, demodulates, and retransmits short duration messages, from sources including tagged marine organisms, autonomous vehicles, subsurface floats, and buoys. The future DAC will collect, store, process, and analyze acquired data, taking advantage of its ability to disseminate data across the stakeholders and the scientific network. Correlation of animal-borne Argos platform locations and oceanographic data will advance fisheries management, ecosystem-based management, monitoring of marine protected areas, and bio-oceanographic research in the face of a rapidly changing environment. For example, correlation of oceanographic data collected by the HSI, geolocated with supplementary images from the RGB camera and fish locations, will provide researchers with near real-time estimates of essential oceanographic variables within areas selected by species of interest.

physics.ao-ph↗

arXiv2022

Weak-star quasi norm attaining operators

For Banach spaces $X$ and $Y$, a bounded linear operator $T\colon X \longrightarrow Y^*$ is said to weak-star quasi attain its norm if the $σ(Y^*,Y)$-closure of the image by $T$ of the unit ball of $X$ intersects the sphere of radius $\|T\|$ centred at the origin in $Y^*$. This notion is inspired by the quasi-norm attainment of operators introduced and studied in \cite{CCJM}. As a main result, we prove that the set of weak-star quasi norm attaining operators is dense in the space of bounded linear operators regardless of the choice of the Banach spaces, furthermore, that the approximating operator can be chosen with additional properties. This allows us to distinguish the properties of weak-star quasi norm attaining operators from those of quasi norm attaining operators. It is also shown that, under certain conditions, weak-star quasi norm attaining operators share numbers of equivalent properties with other types of norm attaining operators, but that there are also a number of situations in which they behave differently from the others.

math.FA↗

arXiv2022

Ego4D: Around the World in 3,000 Hours of Egocentric Video

We introduce Ego4D, a massive-scale egocentric video dataset and benchmark suite. It offers 3,670 hours of daily-life activity video spanning hundreds of scenarios (household, outdoor, workplace, leisure, etc.) captured by 931 unique camera wearers from 74 worldwide locations and 9 different countries. The approach to collection is designed to uphold rigorous privacy and ethics standards with consenting participants and robust de-identification procedures where relevant. Ego4D dramatically expands the volume of diverse egocentric video footage publicly available to the research community. Portions of the video are accompanied by audio, 3D meshes of the environment, eye gaze, stereo, and/or synchronized videos from multiple egocentric cameras at the same event. Furthermore, we present a host of new benchmark challenges centered around understanding the first-person visual experience in the past (querying an episodic memory), present (analyzing hand-object manipulation, audio-visual conversation, and social interactions), and future (forecasting activities). By publicly sharing this massive annotated dataset and benchmark suite, we aim to push the frontier of first-person perception. Project page: https://ego4d-data.org/

cs.CV↗

arXiv2022

Residuality in the set of norm attaining operators between Banach spaces

We study the relationship between the residuality of the set of norm attaining functionals on a Banach space and the residuality and the denseness of the set of norm attaining operators between Banach spaces. Our first main result says that if $C$ is a bounded subset of a Banach space $X$ which admit an LUR renorming satisfying that, for every Banach space $Y$, the operators $T$ from $X$ to $Y$ for which the supremum of $\|Tx\|$ with $x\in C$ is attained are dense, then the $G_δ$ set of those functionals which strongly exposes $C$ is dense in $X^*$. This extends previous results by J.\ Bourgain and K.-S.\ Lau. The particular case in which $C$ is the unit ball of $X$, in which we get that the norm of $X^*$ is Fréchet differentiable at a dense subset, improves a result by J.\ Lindenstrauss and we even present an example showing that Lindenstrauss' result was not optimal. In the reverse direction, we obtain results for the density of the $G_δ$ set of absolutely strongly exposing operators from $X$ to $Y$ by requiring that the set of strongly exposing functionals on $X$ is dense and conditions on $Y$ or $Y^*$ involving RNP and discreteness on the set of strongly exposed points of $Y$ or $Y^*$. These results include examples in which even the denseness of norm attaining operators was unknown. We also show that the residuality of the set of norm attaining operators implies the denseness of the set of absolutely strongly exposing operators provided the domain space and the dual of the range space are separable, extending a recent result for functionals. Finally, our results find important applications, among which we point out that we solve a proposed open problem showing that the unique predual of the space of Lipschitz functions from the Euclidean unit circle fails to have Lindenstrauss property A.

math.FA↗