**[SAL] i-Fitting-Formations on Clifford semigroups | Ana Catarina Monteiro (CEMAT, University of Lisbon)**

6 May 2024 2:00 pm - 3:00 pm

Seminar Room, Building VII

Abstract:

In this talk we will explore a recent joint work with Gracinda Gomes and study the concept of i-Fitting-Formation of Clifford semigroups.

A class of Clifford semigroups closed for idempotent separating quotients and for subdirect products of a finite family of the class with idempotent separating projections is said to be an i-formation of Clifford semigroups. A class of Clifford semigroups closed for normal subsemigroups and for Clifford semigroups generated by two normal subsemigroups of the class is said to be a Fitting class of Clifford semigroups.

Motivated by [3] and [1], in [2] bijections between classes of semigroups, congruences and languages were established using the concepts of i-formation and Fitting class, in particular on Clifford semigroups. A natural next step of this work is the study of i-Fitting-formations of Clifford semigroups, i.e., classes of Clifford semigroups that are simultaneously an i-formation and a Fitting class. Therefore, in this talk, we will look for the corresponding concepts in congruences and languages, by establishing bijections with i-Fitting-formations of Clifford semigroups.

References:

[1] A. Ballester-Bolinches, E. Cosme Llópez, R. Esteban-Romero, and J. Rutten. Formations of monoids, congruences, and formal languages. Scientific Annals of Computer Science, 25:171–209, 2015.

[2] G. M. S. Gomes and A.-C. C. Monteiro. Formations and i-Fitting classes of inverse semigroups, congruences and languages. to appear in Semigroup Forum.

[3] D. Therien. Classification of Regular Languages by Congruences. PhD thesis, 1980. AAI0533628.

**[SOR] Forest management: integrating mixed integer programming and fire spread | Isabel Martins (ISA - University of Lisbon, Portugal)**

8 May 2024 2:00 pm - 3:00 pm

Room 3.3 - VII

Abstract:

A major activity in forest management is planning silviculture activities. Mixed integer programming (MIP) has been used to obtain optimal plans considering management objectives and constraints (e.g. carbon stock, biodiversity, and soil erosion). Our contribution is addressing fire not as an attribute/parameter of the MIP model, but by simulating its spread. Initially, the MIP model is solved. Subsequently, a worst-case fire spread simulation is conducted to identify fire paths with an excessively high rate of spread. Each identified unacceptable path results in an additional constraint in the MIP. This process is repeated until no unacceptable paths are identified, ensuring that no fire paths will have a rate of spread higher than a specified threshold.

**[SAn] Subgaussian Kahane-Salem-Zygmund inequalities in Banach spaces | Mieczysław Mastyło (Adam Mickiewicz University, Poznań, Poland)**

8 May 2024 2:15 pm - 3:15 pm

Room 1.6, building VII.

**Title: **Subgaussian Kahane-Salem-Zygmund inequalities in Banach spaces.

**Speaker**: Mieczysław Mastyło (Adam Mickiewicz University, Poznań, Poland).

**Time: **Wednesday, 8 May 2024, from 14:15 to 15:15.

**Place: **Room1.6, building VII.

**Abstract: **We will discuss approaches to the famous Kahane-Salem-Zygmund inequalities. In particular we will present estimates of the exponential Orlicz norms for $\sup_{1\leq j\leq N}\big|\sum_{i=1}^Ka_i(j) \gamma_i\big|$, where $(a_i(j))_{j=1}^N \in \ell_\infty^N, \,1 \leq i \leq K$ and $(\gamma_i)$ is a sequence of subgaussian random variables. Using tools from probability theory, Banach spaces and interpolation, we obtain new Kahane-Salem-Zygmund type random inequalities for the space of subgaussian polynomials on finite-dimensional Banach spaces, as well as for subgaussian Dirichlet polynomials. The talk is based on joint work with Andreas Defant.

**[SAL] Why does Deep Learning work so well? | Atle Hahn (NOVA Math)**

13 May 2024 2:00 pm - 3:00 pm

Seminar Room, building VII

Deep Neural Networks are at the heart of most recent breakthroughs in Artificial Intelligence. However, not so long ago most AI experts had a rather low opinion about them. For example, Vladimir Vapnik, the founder of the field of "Statistical Learning Theory", predicted in 1995 that by 2005 no one would use neural networks any more.

What was it about neural networks that most experts overlooked at that time? In my talk I will try to answer this question.

The talk is directed to a general audience. No prior knowledge of Machine Learning is required.

**[SAn] Stochastic solutions and singular partial differential equations | Rui Vilela Mendes (CMAFcIO, Faculdade de Ciências, Universidade de Lisboa, Portugal)**

15 May 2024 2:15 pm - 3:15 pm

Room 1.6, building VII.

**Title: **Stochastic solutions and singular partial differential equations.

**Speaker**: Rui Vilela Mendes (CMAFcIO, Faculdade de Ciências, Universidade de Lisboa, Portugal).

**Time: **Wednesday, 15 May 2024, from 14:15 to 15:15.

**Place: **Room 1.6, building VII.

**Abstract: **After a short survey of current results on the stochastic solution approach to nonlinear partial differential equations, it is shown how this method may be extended to obtain solutions of singular pde´s driven by noise. A working suggestion is made on the possible relation of these results to the pathwise rough path methods.

**[SAL] From the extended Schur algebra to the rook monoid | Inês Legatheaux Martins (CMAFcIO, FCUL)**

20 May 2024 2:00 pm - 3:00 pm

DM Meeting Room, Building VII

Abstract:

Schur algebras were defined in 1980 by J. A. Green in a seminal monograph. Given an infinite field $\mathbb{F}$, they provide a natural setting for understanding the (polynomial) representations of the general linear group $GL_d(\mathbb{F})$ and their interactions with those of the symmetric group $S_n$. In particular, they were pivotal for extending the classical Schur-Weyl duality for $GL_d(\mathbb{F})$ and $S_n$ on tensors to positive characteristic.

Recently, we introduced the extended Schur algebra $\mathcal{S}_{\mathbb{F}} (d,\mathbf{n})$ and proved that its module category is equivalent to the category of finite-dimensional polynomial $GL_d(\mathbb{F})$-modules which are homogeneous of degree at most $n$. Provided that $d \geq n$, and $\mathbb{F}$ has characteristic zero, we gave a new instance of Schur-Weyl duality for $\mathcal{S}_{\mathbb{F}} (d,\mathbf{n})$ and an important generalisation of $S_n$ called the rook monoid $R_n$ (also known as the symmetric inverse monoid).

Another upshot of Green’s monograph is the description of several functors relating the module categories of the algebras $A$ and $eAe$, where $e \in A$ is an idempotent. The aim of this talk is to give some applications of this general theory to the modular representation theory of the rook monoid.

Our purpose is to explain how these methods can be used to show that the Schur-Weyl duality between $\mathcal{S}_{\mathbb{F}} (d,\mathbf{n})$ and $R_n$ remains true for an infinite field $\mathbb{F}$ of arbitrary characteristic as well as to give a combinatorial construction of certain $\mathbb{F}R_n$-modules which are analogous to the dual Specht modules for $S_n$. In good characteristic, this construction will form a complete set of simple modules for the rook monoid.

**[SSRM, SOR] Developing Optimization models in urban transportation fleet | Parisa Ahani (NOVA Math)**

22 May 2024 2:00 pm - 3:00 pm

**Title**: Developing Optimization models in urban transportation fleet

**Speaker: Parisa Ahani, NOVA Math**

**Date | Time:** May 22, 2024 | 14h00

**Place: FCT NOVA, VII-Second Floor, Seminar room**

**Abstract****: **Recently, the use of more sustainable forms of transportation such as electric vehicles (EVs) for delivering goods and parcels to customers in urban areas has received more attention from urban planners and private stakeholders. The urban freight transportation sector is examining such a shift toward using electric vehicles, besides current combustion engine vehicles, to deliver goods and services to customers. To contribute toward sustainable transportation in urban logistics, we consider the important factor of decision replacement management and study how to shift toward sustainable modes of transportation, specifically EVs, in an urban area. We will present various optimization frameworks for different vehicle replacement decision problems that can be used by the operators (private and public stakeholders) for a combination of various types of vehicles in their fleet in order to achieve an optimal fleet structure.

**Organizers:** Isabel Natário & Mina Norouzirad & Graça Gonçalves

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/__UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/____UIDP/00297/2020) (Center for Mathematics and Applications)__

**[CourseAL] Lectures on (Noncommutative) Generalized Numerical Semigroups | Mahir Bilen Can (Tulane University, Louisiana, USA)**

27 May 2024 2:00 pm - 3:00 pm

DM Meeting room, building VII

Numerical semigroups, due to their inherent simplicity, find applications across various branches of mathematics. Despite their straightforward definition, they possess a depth of complexity comparable to that of integer partitions. One of the many reasons they are still actively studied is their natural appearance in the study of algebraic curves. In this lecture series on numerical semigroups, we aim to accomplish two goals:

- Review some geometric constructions of (generalized) numerical semigroups with an eye towards applications (Lecture 1).
- Introduce a theory of non-commutative numerical semigroups related to algebraic groups (Lecture 2).

**[SAn] Leading Eigenvector Dynamics in Brain Signals | Joana Ribeiro Barbosa Cabral (University of Minho, Portugal)**

29 May 2024 2:15 pm - 3:15 pm

Room 1.6, building VII.

**Title: **Leading Eigenvector Dynamics in Brain Signals.

**Speaker**: Joana Ribeiro Barbosa Cabral (University of Minho, Portugal).

**Time: **Wednesday, 29 May 2024, from 14:15 to 15:15.

**Place: **Room 1.6, building VII.

**Abstract: **Brain activity at rest exhibits the temporary formation of macroscale activity patterns, during which the signals in distinct brain areasco-fluctuate together forming coupling modes with functional relevance. These patterns are consistently detected in human resting-state fMRI and appear altered in a wide range of psychiatric conditions, pointing to close relation with brain function.

Among the diversity of analysis methods to quantify the expression of these patterns and evaluate differences between conditions, a particular algorithm, termed Leading Eigenvector Dynamics Analysis (LEiDA) is demonstrating growing potential given its remarkable sensitivity and demonstrated replicability, capturing alterations between psychiatric, pharmacological, psychological and even task conditions.

In my talk, I will explain the foundations of the LEiDA algorithm and provide an overview of its applications. Finally, I will share the controversial insights that LEiDA is revealing into brain activity, provoking a paradigm shift in our understanding of brain function.

**[SSRM] PhD Program in Mathematics Seminars | Mafalda Ferreira and Nadia Bachir (PDM & NOVA Math)**

29 May 2024 2:30 pm - 3:30 pm

**Title1**: Machine learning to predict and optimize energy profile consumption in green data centers

**Title2**: Statistical and Deep Learning for Complex Spatio-temporal Fire Data

**Speaker: Mafalda Ferreira & Nádia Bachir, PDM & NOVA Math**

**Date | Time:** May 29, 2024 | 14h30

**Place: FCT NOVA, VII-3.3**

**Abstract1****: **As the Internet experiences exponential growth and usage, the power consumption of data centers has increased considerably. The electricity consumption in global data centers range between 1.1% and 1.5% of total electricity usage. In this way, renewable energy sources present a promising solution to mitigate the environmental footprint of data center operations. The focus of this study consists of combining a prediciton and an optimization framework regarding the energy consumption of green data centers. We will present the proposed plan of this study, as well as some state of the art approaches that can be useful in a near future.

**Abstract2****: ** This study focuses on modelling complex spatio-temporal fire data using marked spatiotemporal point processes, extreme value theory and Deep Learning methods under a Bayesian framework. By working with both, forest and urban fires in Portugal, the goal is to model and compare the dynamics of events between the two systems.

Another goal concerns the definition of extreme/non-extreme events for forest and urban areas and employing the Integrated Nested Laplace Approximation (INLA) and Deep Learning algorithms to maximize the accuracy.

In conclusion, the study aims to provide a comprehensive framework for modeling and analyzing complex spatio-temporal fire data, to promote better fire management practices and improve overall public safety.

**Organizers:** Isabel Natário & Mina Norouzirad & Regina Bispo

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (__https://doi.org/10.54499/UIDB/00297/2020__) and UIDP/00297/2020 (

__https://doi.org/10.54499/__) (Center for Mathematics and Applications)

__UIDP/00297/2020__**[CourseAL] Lectures on (Noncommutative) Generalized Numerical Semigroups | Mahir Bilen Can (Tulane University, Louisiana, USA)**

3 June 2024 2:00 pm - 3:00 pm

DM Meeting room, building VII

Numerical semigroups, due to their inherent simplicity, find applications across various branches of mathematics. Despite their straightforward definition, they possess a depth of complexity comparable to that of integer partitions. One of the many reasons they are still actively studied is their natural appearance in the study of algebraic curves. In this lecture series on numerical semigroups, we aim to accomplish two goals:

- Review some geometric constructions of (generalized) numerical semigroups with an eye towards applications (Lecture 1).
- Introduce a theory of non-commutative numerical semigroups related to algebraic groups (Lecture 2).

**[SMHealth] Short-Course of Mathematics for Health**

4 June 2024 10:00 am - 12:00 pm

Seminar Room, Building VII, Mathematics Department

**4 - 5 June, 10:00 – 12:00 and 14:00 – 16:00, TBA**

Short-Course Title: On Simulation Guided Clinical Trial Designs

#### Rajat Mukherjee

#### Founder and Chief Statistical Consultant Mukherjee-Consultants, Barcelona, Spain

**[SMHealth] Short-Course of Mathematics for Health**

4 June 2024 2:00 pm - 4:00 pm

Seminar Room, Building VII, Mathematics Department

4 - 5 June, 10:00 – 12:00 and 14:00 – 16:00, Room TBA

Short-Course Title: On Simulation Guided Clinical Trial Designs

Rajat Mukherjee

Founder and Chief Statistical Consultant Mukherjee-Consultants, Barcelona, Spain

**[SMHealth] Short-Course of Mathematics for Health**

5 June 2024 10:00 am - 12:00 pm

Seminar Room, Building VII, Mathematics Department

4 - 5 June, 10:00 – 12:00 and 14:00 – 16:00, Room TBA

Short-Course Title: On Simulation Guided Clinical Trial Designs

__Rajat Mukherjee__

Founder and Chief Statistical Consultant Mukherjee-Consultants, Barcelona, Spain

**[SMHealth] Short-Course of Mathematics for Health**

5 June 2024 2:00 pm - 4:00 pm

Seminar Room, Building VII, Mathematics Department

4 - 5 June, 10:00 – 12:00 and 14:00 – 16:00, Room TBA

Short-Course Title: On Simulation Guided Clinical Trial Designs

__Rajat Mukherjee__

Founder and Chief Statistical Consultant Mukherjee-Consultants, Barcelona, Spain

**[SMHealth] Seminar of Mathematics for Health**

6 June 2024 3:00 pm - 4:00 pm

Seminar Room, Building VII, Mathematics Department

#### 6 June, 15:00, Room TBA

#### Seminar title: Adaptive Risk-Mitigated Designs for Machine Learned Diagnostic Devices

**Rajat Mukherjee**

#### Founder and Chief Statistical Consultant Mukherjee-Consultants, Barcelona, Spain

Abstract em https://eventos.fct.unl.pt/novamath_thematic_weeks/pages/seminars

**[SMHealth] Coffee Break of Mathematics for Health**

6 June 2024 4:00 pm - 5:30 pm

Seminar Room, Building VII, Mathematics Department

Seminar Discussion & Coffee break

**[SSRM] Advancing Glioma Research through Multi-Omics Network Discovery and Patient Stratification: Insights from the MONET Project | Roberta Coletti (NOVA Math)**

12 June 2024 2:00 pm - 3:00 pm

**Statistics and Risk Management Seminar**

**Department of Mathematics, NOVA MATH/FCT NOVA**

**Title**: Advancing Glioma Research through Multi-Omics Network Discovery and Patient Stratification: Insights from the MONET Project

**Speaker: Roberta Coletti**, NOVA Math

**Date | Time:** June 12, 2024 | 14h00

**Place: FCT NOVA, VII-Second Floor, Seminar room**

**Abstract****: **Gliomas are primary malignant brain cancers characterized by high heterogeneity. The different glioma types present distinct molecular characteristics, which affect patient prognosis and treatment responses. The work being discussed in this talk is part of the MONET project, which aims to explore the molecular diversity of gliomas through multi-omics data analysis, in order to identify possible biomarkers explaining cancer heterogeneity. In particular, the presented study was focused on network discovery and exploration, which was later used to perform additional research tasks, such as variable selection, patients’ classification, and survival analysis. The obtained results will be presented and discussed in terms of their potential biological and clinical application.

**Short Bio:** Roberta Coletti studied mathematics from the University of Rome, La Sapienza. She completed a PhD in mathematics at the University of Trento, with a thesis on ordinary differential equation models of prostate cancer immunotherapy. Currently, she is a researcher at the Center for Mathematics and Applications at NOVA University of Lisbon. Her work focuses on identifying molecular biomarkers for glioma cancer by analyzing large multi-omics datasets using statistical and machine learning methods.

**Organizers:** Isabel Natário & Mina Norouzirad & Marta Lopes

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/__UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/____UIDP/00297/2020) (Center for Mathematics and Applications)__

**[CourseAL] Planar maps, bent functions over finite fields, and an uncertainty principle | Ferruh Özbudak (Middle East Technical University)**

14 June 2024 2:00 pm - 4:00 pm

Room 1.5, Building VII

Abstract:

We explain some fundamental facts on planar maps and bent functions over finite fields. We also explain some connections to other areas. Also, a short introduction to the uncertainty principle of discrete Fourier transform will be presented.

**[SOR] Extensions and variational formulations of the cp-rank | Immanuel M. Bomze (Department of Statistics and Operations Research (ISOR))**

17 June 2024 2:00 pm - 3:00 pm

Room 2.2 VII

Abstract: This is a progress report on two separate research projects, both concerned with studies on the cp-rank, a matrix parameter which plays a crucial role in conic optimization used for tight bounds of hard problems. In the symmetric case, lower and upper bounds in (quadratic) terms of the order are known which are asymptotically tight.

We will discuss an extension to non-symmetric square matrices and characterize it by a variational formulation. This results in a QCQP under conic constraints. Going back to the original concept of cp-rank for symmetric matrices, we will show by example that the standard Burer relaxation of the quadratic and linear constraints will yield useless bounds.

**[CourseAL] b-Symbol weight of codes, bounds, weight distributions, and cyclic codes | Ferruh Özbudak (Middle East Technical University)**

17 June 2024 2:00 pm - 4:00 pm

Room 1.5, Building VII

Abstract:

Symbol-pair weight of codes is a recent concept with applications, for example, in read memory channels. This concept is generalized to b-symbol weight in the literature as well. We present an overview of some of the recent results including bounds and connections to cyclic codes.

**[Short-courseDataScience] Causal inference in drug discovery | Tom Michoel (University of Bergen)**

18 June 2024 10:00 am - 12:00 pm

Seminar room, 2nd floor, building VII | NOVA FCT

**[SSRM] PhD Program in Mathematics Seminars | André Folgado, Laura Manteigas & Ricardo Coelho (PDM & NOVA Math)**

18 June 2024 4:00 pm - 5:00 pm

**Titles:**

**Title 1:** Bayesian Inference in Multivariate MSV models

**Title 2:** Monte Carlo Simulation Study using bayesian time series model for energy hedging strategies

**Title3:** Using Satellite Earth Observations for Estimation Biomass

**Speakers:** Laura Manteigas, André Folgado & Ricardo Coelho, PDM & NOVA Math

**Date | Time:** June 18, 2024 | 16h**Place:** FCT NOVA, VII-Second Floor, Seminar room

**Abstracts:**

**Abstract 1:** Financial time series frequently exhibit serially correlated changes in volatility. While this has led to significant research on multivariate ARCH models, MSV models offer significant statistical benefits. Thereby, this study aims to examine temporal volatility patterns through the latter. The research will employ Bayesian MCMC methodology to estimate MSV models, providing a more comprehensive understanding of the multivariate volatility dynamics (e.g., by deriving the posterior distributions for model parameters and studying the complex relationships between the series). Specifically, it aims to investigate volatility patterns in the emerging markets of the EU (as classified by MSCI) across three distinct periods: before, during, and after the COVID-19 pandemic.

**Abstract 2:** The main objective of this study is to develop a Bayesian time series model for energy hedging strategies. The model will be used to generate scenarios for renewable asset generation. Asset historical data will be used and other relevant exogenous variables such as wind speed, irradiation and temperature when available. Using Monte Carlo simulation, the model will provide sensible medium/long term scenarios for energy generation, allowing to understand cluster's characteristic distributions and the overall agent's risk exposure to generation risk. The model will be validated analysing if covariances and correlations are consistent with historical data. The study will contribute to the existing literature on energy hedging strategies and will provide valuable insights for energy companies to manage their risk exposure.

**Abstract 3: **The importance of quantifying and monitoring the amount of carbon in forest is crucial to define global policies, understand climate change and help with the emerging market in carbon credits. The quantification of the amount of carbon can be done through the quantification of biomass, since they have the following relationship: Carbon = 0.5×AGB, AGB being the above ground biomass. The estimation of AGB can be done through indirect methods that don’t destroy trees in the process. For example, using statistical models for biomass data collected in forest inventories, which are expensive and time-consuming processes. An alternative brought by technology is remote sensing estimation, collecting remote data, namely through satellites, which can be used in conjunction with terrestrial observations. This can contribute to faster, cheaper and more accurate estimation of AGB. In recent years, machine learning models and statistical models have been applied using the Frequentist approach as well as the Bayesian approach. However, models using the Bayesian approach have obtained better predictive results compared to models using the Frequentist approach. In this work, we use the Bayesian approach applied to Geostatistical modeling, since the response variable (AGB) is a continuous spatial phenomenon in a domain and is observed in a finite number of fixed points. The area of interest for this work is the Palentina Mountain (Monta ̃na Palentina), where we will estimate the AGB only in the forested areas of this region. Palentina Mountain is an area belonging to the Atlantic Forest in northern Spain. To estimate the AGB we use field data, coming from the Fourth National Forest Inventory of Spain as well as remote data, provided by GEOSAT-2 satellite. Remote data are extracted from the reflectance bands, where measures of interest such as vegetation indices, texture and spectral variables can be extracted. In addition land variables such as Slope, Altitude, Orientation, species of the trees, among others are also used.

**Bios:**

**Bio1:** Laura is a Mathematics PhD student. Prior to this, she took a Master's in Applied Mathematics and a Bachelor's in Mathematics.

**Bio2:** Andre L. Folgado is a Ph.D. student in the Department of Mathematics at NOVA School of Science and Technology in Caparica, Portugal. He has a Bachelor and Master's degree in Mechanical Engineering from Instituto Superior Técnico, University of Lisbon. He is a professional with experience in the energy sector, having worked as a consultant in the energy markets for IHS Markit in London, UK. Currently, he is working in EDP's Global Energy Management division, focusing on Advancing Analytics. His research interests include energy markets, risk management and portfolio evaluation.

**Bio3:** Ricardo Coelho is a first-year PhD student in the Mathematical Doctoral Programme at the NOVA School of Science and Technology (FCT-NOVA). His research work is focused on predicting forest biomass, through statistical models, using field and remote sensing data. Before enrolling in his PhD, he did a MSc in Mathematics and Applications at FCT-NOVA and a BSc in Mathematics at the same University.

**Organizers:** Isabel Natário & Mina Norouzirad & Regina Bispo

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (__ https://doi.org/10.54499/UIDB/00297/2020__) and UIDP/00297/2020 (

__) (Center for Mathematics and Applications)__

__https://doi.org/10.54499/____UIDP/00297/2020__**[Short-courseDataScience] Causal inference in drug discovery | Tom Michoel (University of Bergen)**

19 June 2024 10:00 am - 12:00 pm

Seminar room, 2nd floor, building VII | NOVA FCT

**[SAn] How the maximal operator's self-improving property translates into spaces of homogeneous type | Alina Shalukhina (Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Portugal)**

19 June 2024 2:15 pm - 3:15 pm

Room 1.6, building VII

**Title: **How the maximal operator's self-improving property translates into spaces of homogeneous type.

**Speaker**: Alina Shalukhina (Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Portugal).

**Time: **Wednesday, 19 June 2024, from 14:15 to 15:15.

**Place: **Room 1.6, building VII.

**Zoom Link: **https://videoconf-colibri.__zoom.us/j/93912858550?pwd=____oiss4uahs9EiSqV52OwIsblRIZlGbs____.1__

**Abstract: **We prove the self-improvement property of the Hardy–Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type—it is this accomplishment that is the focus and motive of the talk. Our result is a generalization of the boundedness criterion obtained in 2010 by Lerner and Ombrosi for maximal operators on quasi-Banach function spaces over Euclidean spaces. The specialty of the proof for spaces of homogeneous type lies in using adjacent grids of Hytönen–Kairema dyadic cubes and studying the maximal operator alongside its "dyadic" version; we will look into these technical curiosities in detail. Then we apply the obtained result to variable Lebesgue spaces over spaces of homogeneous type.

**[SDataScience] Intelligent systems for risk prediction and diagnosis of non-communicable diseases | Tom Michoel (University of Bergen)**

19 June 2024 2:30 pm - 4:00 pm

Room 1.3, 1st Floor, Building VII

**[Bio] A mathematical modelling perspective on immune-mediated disorders, AJ Soares (UMinho)**

19 June 2024 4:00 pm - 5:30 pm

Seminar room, 2nd floor, building VII | NOVA FCT

**[Bio Short-course] On the mathematical modelling of immune systems disorders, AJ Soares (UMinho)**

20 June 2024 10:00 am - 12:00 pm

Seminar room, 2nd floor, building VII | NOVA FCT

**[CourseAL] Automated Theorem Proving and Algebra | Michael Kinyon (University of Denver)**

20 June 2024 2:00 pm - 4:00 pm

Room 1.5, Building VII.

Abstract:

This mini-course will introduce the audience to automated theorem proving (ATP) using Prover9. While ATP can, in principle, be used in any area of mathematics which has questions with first-order formulations, it has been particularly successful in various branches of algebra, such as quasigroup theory, lattice theory, semigroup theory, etc.

On the first day, I will discuss the basics of ATP systems and how they work, of setting up Prover9 input files, and some of the various settings. On the second day, I will discuss more advanced techniques, such as semantic guidance and proof sketches. One of the morals of the story I hope to tell is that an ATP system is not just a black box, but a tool you can use effectively to help you in your own research.

**[Bio Short-course] On the mathematical modelling of immune systems disorders, AJ Soares (UMinho)**

20 June 2024 2:00 pm - 4:00 pm

Seminar room, 2nd floor, building VII | NOVA FCT

**[Bio Short-course] On the mathematical modelling of immune systems disorders, AJ Soares (UMinho)**

21 June 2024 10:00 am - 12:00 pm

Seminar room, 2nd floor, building VII | NOVA FCT

**[CourseAL] Automated Theorem Proving and Algebra | Michael Kinyon (University of Denver)**

21 June 2024 2:00 pm - 4:00 pm

Room 1.5, Building VII

Abstract:

This mini-course will introduce the audience to automated theorem proving (ATP) using Prover9. While ATP can, in principle, be used in any area of mathematics which has questions with first-order formulations, it has been particularly successful in various branches of algebra, such as quasigroup theory, lattice theory, semigroup theory, etc.

On the first day, I will discuss the basics of ATP systems and how they work, of setting up Prover9 input files, and some of the various settings. On the second day, I will discuss more advanced techniques, such as semantic guidance and proof sketches. One of the morals of the story I hope to tell is that an ATP system is not just a black box, but a tool you can use effectively to help you in your own research.

**[SAL] Free growth, free counting | Carl-Fredrik Nyberg Brodda (Korea Institute for Advanced Study)**

24 June 2024 2:00 pm - 3:00 pm

I will discuss some recent forays into some counting problems for free objects. I will focus on free inverse semigroups and free regular ∗-semigroups. I will first discuss recent results joint with M. Kambites, N. Szakács, and R. Webb giving a precise rate of exponential growth of the free inverse monoid of arbitrary (finite) rank, which turns out to be given by a surprisingly complicated but algebraic number. I will then discuss a useful tool for counting algebraic things – rewriting systems – and an elegant bijection which proves a surprising result about the rate of growth of the monogenic free regular ∗-semigroup. Then, and again using the theory of rewriting systems, I will discuss just how non-finitely presented some of these free objects are, and some homological corollaries.

**[SAL] Pythagorean Triples via Multiplicative Functions | Guilherme Azevedo (NOVA FCT / NOVA Math)**

26 June 2024 2:00 pm - 3:00 pm

Zoom link: https://videoconf-colibri.zoom.us/j/92954771613

Suppose that the natural numbers are coloured with a finite number of colours. The question whether there are solutions to the equation x^2+y^2=z^2 where x,y,z all have the same colour remains unanswered to this day. This was first asked by Erdős and Graham in the late 70's, and it is colloquially referred to as the Pythagorean triples (colouring) problem. Motivated by multiplicative functions, we explore some state-of-the-art results that lend support to the hypothesis that the answer to the Pythagorean triples problem is affirmative.

**[SAn] Sandra Thampi (Universidade NOVA de Lisboa, NOVA Math, Portugal) and Márcio Valente (NOVA School of Science and Technology, Universidade NOVA de Lisboa, NOVA MATH - Center for Mathematics and Applications, Portugal)**

4 July 2024 10:00 am - 12:00 pm

**Speaker: **Sandra Thampi (Universidade NOVA de Lisboa, NOVA Math, Portugal).

**Title: **Fredholm theory of discrete Wiener-Hopf operators on Orlicz sequence spaces.

**Time: **Thursday, 4 July 2024, from 10h00 to 10h50.

**Place: **https://videoconf-colibri.zoom.us/j/92219333954?pwd=BrsfbKDEVGddzLiWbdEpoEex4NSawC.1

**Abstract: **We extend the Fredholm criteria for discrete Wiener-Hopf operators with continuous symbols on the Lebesgue sequence spaces to the setting of reflexive Orlicz sequence spaces. We combine these results with some Banach algebra techniques to obtain a Fredholm criteria for any operator in the closed subalgebra generated by the discrete Wiener-Hopf operators with continuous symbols. Additionally, we study the Fredholm theory of discrete Wiener-Hopf operators with symbols from Douglas-type algebra and study the algebra generated by them. Finally, we present a local principle for assessing the Fredholmnessof discrete Wiener-Hopf operators.

**Speaker: **Márcio Valente (NOVA School of Science and Technology, Universidade NOVA deLisboa, NOVA MATH - Center for Mathematics and Applications, Portugal).

**Title: **Fredholm theory for Wiener-Hopf integral operators on Orlicz spaces.

**Time: **Thursday, 4 July 2024, from 11h00 to 11h50.

**Place: **https://videoconf-colibri.zoom.us/j/92219333954?pwd=BrsfbKDEVGddzLiWbdEpoEex4NSawC.1

**Abstract: **We extend the Fredholm criteria for Wiener-Hopf operators with continuous symbols on the Lebesgue space L

^{𝑝}(ℝ

_{+}), 𝑝∈(1,∞), obtained by Roland Duduchava in the late 1970s, to the setting of reflexive Orlicz spaces L

^{𝛷}(ℝ

_{+}). Following this, we formulate a conjecture which seeks to refine this result by removing the reflexivity assumption.

After this, we introduce the algebra of piecewise continuous symbols and obtain some preliminary results which in turn will lead towards the rediscovery of the Fredholm criteria for Wiener-Hopf operators with piecewise continuous symbols on the Lebesgue space L

^{𝑝}(ℝ

_{+}), 𝑝∈(1,∞), which was also obtained by Roland Duduchava. Finally, a conjecture is presented as we try to extend this result to the setting of Orlicz spaces.

**Keywords: **Fourier multiplier, Wiener-Hopf operator, Fredholm criteria, Orlicz space.

**[SOR] Considerations of Sustainability in Transportation - A Case for Multi-objective Optimisation | Judith Wang (School of Civil Engineering and Institute for Transport Studies, University of Leeds)**

9 July 2024 2:00 pm - 3:30 pm

Sala de Seminários _ VII

Abstract: Traditionally, optimisation models used in transportation planning consider the optimisation of economic objectives such as minimising travel distance, travel time and monetary cost or maximising the more abstract concept of "utility". However, transportation is not a purely economic activity. It affects people and the environment in many ways, e.g., through fuel consumption and pollution. Hence decision makers at all levels - from a worker choosing a route for his commute to work to a national government aiming to reduce greenhouse gas emissions - are increasingly interested to pursue aims that fall under the wide umbrella of sustainability when making transport decisions. In this talk, we present four examples that illustrate how multi-objective optimisation can be a valuable tool to support decision making for sustainable transport.

Keywords: Transportation, Health, Reliability, Sustainability, Shortest Path, Traffic Assignment, Bi-level Optimisation, Multi-objective Optimisation

**Healthy Route Choice for Commuter Cyclists**

Commuter cyclists are often motivated by health benefits of cycling, yet they are vulnerable to exposure to traffic-related air pollution. Hence, in their route choice they face trade-offs between travel time and pollutant dose. We develop a bi-objective shortest path model, which considers the minimisation of travel time and pollutant dose. Travel time takes into account the length and slope of each link on a path as well as the average speed of the cyclist. Pollutant dose is calculated based on traffic flow, speed and vehicle fleet composition. Using a vehicle emissions prediction model these are converted to pollutant concentrations and multiplied by travel time and cyclist minute ventilation rate finally result in pollutant dose values for each link. Since both travel time and pollutant dose are additive, we can employ a bi-objective label correcting algorithm to find the set of efficient paths from which the cyclist can choose. The model is applied in a case study in Auckland, New Zealand.

**Walking School Bus Line Routing for Efficiency, Health and Walkability**

Walking School Bus (WSB) has been recognised as an innovative solution to promote walking to school, bringing a wide spectrum of benefits, including: health benefits from the physical exercise, social skills and traffic reduction. To facilitate the success of WSBs, one vital element is its route planning, which directly affects the catchment for the service and the realisation of all the potential benefits. Previously, time has been the only factor that has been considered in WSB routing problems. Other important factors including air quality, safety and comfort will also be considered in this paper. Air quality along a WSB route is important to help realise the health benefits of walking. Traffic safety has been the biggest barrier to walking to school and must be addressed in planning a WSB route. Ensuring children have an enjoyable and comfortable experience is vital for the sustainability and success of WSB.

A walking network is introduced to enable modelling pedestrian movements in detail, including walking movements on different sides of the road and crossing movements. This approach enables detailed route-based analysis to assess the localised effect of air quality on pollutant dose. We define walkability as a measure of children’s needs in safety and comfort, which can also be assessed in detail on each route. We propose a multi-objective optimisation model to generate *efficient* WSB routes with three objectives representing the potential benefits of WSB: (1) to minimise time; (2) to minimise pollutant dose; and (3) to maximise walkability. Our multi-objective WSB route planning model is highly transferable to any selected school in any WSB targeted area. Planners will be able to select a combination of WSB lines to offer, based on the requirement of coverage area and resource availability.

**Bi-objective User Equilibrium Models of Travel Time Reliability**

Models of route choice are also central to user equilibrium models in traffic assignment. Traffic assignment is concerned with determining how traffic flow satisfying demand for a certain number of trips between origins and destinations in a road network is distributed on the links of this network. This results in equilibrium models, where at equilibrium no user (driver) has an incentive to unilaterally switch routes, because all traffic is on "minimum cost'' routes. So what does "minimum cost'' mean? Empirical studies have shown that the three most important factors that influence route choice behaviour of drivers are travel time, travel time reliability and monetary cost. In many models considering these factors, a generalised cost function making use of values of time and/or values of reliability (possibly for different user classes) is considered as the route choice function, i.e., it is assumed that all drivers aim to minimise their generalised cost when choosing a route from their origin to their destination. In contrast we introduce a definition of bi-objective user equilibrium.

We show that the earlier concepts of travel-time-budget user equilibrium and late-arrival-penalty user equilibrium are special cases of this definition. In fact, the definition of bi-objective user equilibrium gives rise to a set of TTR-BUE flows, and generalised cost user equilibrium flows are specific TTR-BUE flows.

**Road Pricing for Sustainability**

Congestion pricing is a policy instrument that is used in many cities around the world, e.g., Singapore, London and Stockholm, to reduce congestion of the road network during peak hours. But it is also part of wider strategies to enhance sustainability in transport. It can improve the environment in terms of air quality and hence reduce the negative impact of vehicle emissions on health. From an optimisation point of view, to maximise the effectiveness of congestion pricing, it is only natural to consider internalising the external costs of air pollution, including costs associated with their impact on the environment and population health, by charging road users an appropriate toll.

We consider a bi-level multi-objective model to achieve this goal. The upper level models the decision making process of the policy decision makers, which are to minimise total travel time, to minimise total vehicle emissions and to minimise negative impact on health modelled as, for example, median population CO dose. Thus at the upper level we consider a three-objective optimisation problem to determine link tolls for all links in the network.

**[SOR] Distance Geometry and Molecular Optimization | Carlile Lavor (University of Campinas, Brazil)**

10 July 2024 2:00 pm - 3:00 pm

2.1 VII

Abstract: The main problem of Distance Geometry can be defined as an inverse problem: given some distances between pairs of objects, determine their positions in some geometric space. Among countless applications, including astronomy, statistics, nanotechnology, robotics and telecommunications, the calculation of the 3D structure of protein molecules (the "molecules of life") stands out, known in the literature as the Molecular Distance Geometry Problem (MDGP). Due to its chemical and geometric properties, the MDGP can be "solved" by a Branch & Prune (BP) method. In the lecture, we will talk a little about BP and some more recent results on the topic.

**[SSRM] PhD Program in Mathematics Seminars | Laura Manteigas (PDM & NOVA Math)**

10 July 2024 4:00 pm - 5:00 pm

**Title:** Bayesian Inference in Multivariate MSV models

**Speaker:** Laura Manteigas, PDM & NOVA Math

**Date | Time:** July 10, 2024 | 16h**Place:** FCT NOVA, VII-2.1

**Abstract:** Financial time series frequently exhibit serially correlated changes in volatility. While this has led to significant research on multivariate ARCH models, MSV models offer significant statistical benefits. Thereby, this study aims to examine temporal volatility patterns through the latter. The research will employ Bayesian MCMC methodology to estimate MSV models, providing a more comprehensive understanding of the multivariate volatility dynamics (e.g., by deriving the posterior distributions for model parameters and studying the complex relationships between the series). Specifically, it aims to investigate volatility patterns in the emerging markets of the EU (as classified by MSCI) across three distinct periods: before, during, and after the COVID-19 pandemic.

**Bio:** Laura is a Mathematics PhD student. Prior to this, she took a Master's in Applied Mathematics and a Bachelor's in Mathematics.

**Organizers:** Isabel Natário & Mina Norouzirad & Regina Bispo

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (__https://doi.org/10.54499/UIDB/00297/2020__) and UIDP/00297/2020 (

__) (Center for Mathematics and Applications)__

__https://doi.org/10.54499/____UIDP/00297/2020__**[SAn] The numerical study of a class of singular fractional differential equations | Ghulam Abbas Khan (Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Portugal)**

17 July 2024 2:15 pm - 3:15 pm

Room 1.6, building VII.

**Title: **The numerical study of a class of singular fractional differential equations.

**Speaker**: Ghulam Abbas Khan (Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Portugal).

**Time: **Wednesday, 17 July 2024, from 14:15 to 15:15.

**Place: **Room 1.6, building VII.

**Abstract: **See attachment.

**[SAn] Nyström methods for Fredholm integral equations defined on planar domains | Maria Grazia Russo (Department of Engineering, University of Basilicata, Italy)**

25 September 2024 2:15 pm - 3:15 pm

Room 1.6, building VII.

**Title:** Nyström methods for Fredholm integral equations defined on planar domains.

**Speaker**: Maria Grazia Russo (Department of Engineering, University of Basilicata, Italy).

**Time: **Wednesday, 25 September 2024, from 14:15 to 15:15.

**Place: **Room1.6, building VII.

**Abstract: **The talk is devoted to a general Nyström scheme for approximating bivariate linear integral equations of the second kind defined on suitable domains of the plane.

The basic idea of the numerical strategy is to use a global approach, that is to use cubature rules built starting from a polynomial approximation scheme.

In fact, the global approximation allows to obtain excellent convergence results, since the order of convergence of the corresponding Nyström methods, is the same as the best polynomial approximation of the solution in suitable selected spaces of functions. Furthermore, in this context it is quite easy to prove the stability of the methods and the good conditioning of the involved linear systems.

We will give an overview of several results obtained in the last few years, starting from rectangular bounded or unbounded domains, also in the case where the known functions of the equation may have singularities on the boundaries, and arriving at the case of equations defined on curvilinear domains.

**[Mini-courseAn] Numerical methods for delay and fractional differential equations | Neville J. Ford (University of Chester, UK)**

16 October 2024 2:15 pm - 4:15 pm

Room 1.4, building VII.

**Title: **Numerical methods for delay and fractional differential equations.

**Speaker**: Neville J. Ford* (University of Chester, UK).

**Date| Time: **Wednesday, 16 October 2024, from 14:15 to 16:15 - Room 1.4, building VII.

**Abstract: **We will consider how to solve delay differential equations and fractional differential equations using numerical schemes. To understand how to do this, we will begin by considering the fundamental theory associated with these equations. We look at the dimension of the underlying dynamical systems to explain how approximation schemes should be set up, and how their performance should be judged. In particular, we shall look at initial and boundary conditions needed to ensure a unique solution and we will see how these must be related to the numerical schemes. If time permits, we shall consider some fractional problems with delays and see how the insights from both types of problems combine in this case.

*https://www.researchgate.net/profile/Neville-Ford

**[SOR] Enhancing the Efficiency and Stability of Deep Neural Network Training through Controlled Mini-batch Algorithms | Corrado Coppola (Sapienza University of Rome, Italy)**

16 October 2024 4:15 pm - 5:15 pm

Room 1.11 - VII

Enhancing the Efficiency and Stability of Deep Neural Network Training through

Controlled Mini-batch Algorithms

The exponential growth of trainable parameters in state-of-the-art deep neural networks

(DNNs), driven by innovations such as self-attention layers and over-parameterization, has led

to the development of models containing billions or even trillions of parameters. As training

datasets grow larger and tasks become more complex, the current challenge lies in balancing

convergence guarantees with the increasing need for efficient training. In this work, we focus on

supervised deep learning, where the training problem is formulated as the unconstrained

minimization of a smooth, potentially non-convex objective function with respect to network

weights.

We propose an approach based on Incremental Gradient (IG) and Random Reshuffling (RR)

algorithms, enhanced with derivative-free extrapolation line-search procedures. Specifically, we

present the Controlled Mini-batch Algorithm (CMA), proposed in [1], which incorporates

sufficient decrease conditions for the objective function and allows for line-search procedures to

ensure convergence, without assuming any further hypotheses on the search direction. We also

present computational results on large-scale regression problems.

We further introduce CMA Light, proposed in [2], an enhanced variant of CMA with

convergence guarantees within the IG framework. Using an approximation of the real objective

function to verify sufficient decrease, CMA Light drastically reduces the number of function

evaluations needed and achieves notable performance gains. We discuss computational results

both against CMA and against state-of-the-art optimizers for neural networks, showing a

significant advantage of CMA Light in large-scale classification tasks using residual

convolutional networks.

Finally, we present the Fast-Controlled Mini-batch Algorithm (F-CMA), extending the

convergence theory of CMA Light to the case where samples are reshuffled at each epoch. We

develop a new line-search procedure, and demonstrate F-CMA's superior performance when

training ultra-deep architectures, such as transformers SwinB and SwinT with up to 130 millions

of trainable parameters. Our results show significant advantages in both stability and

generalization compared to state-of-the-art deep learning optimizers.

**[Mini-courseAn] Numerical methods for delay and fractional differential equations | Neville J. Ford (University of Chester, UK)**

18 October 2024 2:15 pm - 4:15 pm

Room 3.2, building VII.

**Title: **Numerical methods for delay and fractional differential equations.

**Speaker**: Neville J. Ford* (University of Chester, UK).

**Date| Time: **Friday, 18 October 2024, from 14:15 to 16:15 - Room 3.2, building VII.

**Abstract: **We will consider how to solve delay differential equations and fractional differential equations using numerical schemes. To understand how to do this, we will begin by considering the fundamental theory associated with these equations. We look at the dimension of the underlying dynamical systems to explain how approximation schemes should be set up, and how their performance should be judged. In particular, we shall look at initial and boundary conditions needed to ensure a unique solution and we will see how these must be related to the numerical schemes. If time permits, we shall consider some fractional problems with delays and see how the insights from both types of problems combine in this case.

**[SAn] A mathematical framework for dynamical social interactions with dissimulation | Max O. Souza (Center for Mathematics and Applications (NOVA Math), NOVA FCT, Universidade NOVA de Lisboa, Portugal)**

23 October 2024 2:15 pm - 3:15 pm

Room 1.6, building VII.

**Title: **A mathematical framework for dynamical social interactions with dissimulation.

**Speaker**: Max O. Souza (Center for Mathematics and Applications (NOVA Math), NOVA FCT, Universidade NOVA de Lisboa, Portugal).

**Time: **Wednesday, 23 October 2024, from 14:15 to 15:15.

**Place: **Room 1.6, building VII.

**Abstract: **Modeling social interactions is a challenging task that requires flexible frameworks. For instance, dissimulation and externalities are relevant features influencing such systems --- elements that are often neglected in popular models. This paper is devoted to investigating general mathematical frameworks for understanding social situations where agents dissimulate, and may be sensitive to exogenous objective information. Our model comprises a population where the participants can be honest, persuasive, or conforming. Firstly, we consider a non-cooperative setting, where we establish existence, uniqueness and some properties of the Nash equilibria of the game. Secondly, we analyze a cooperative setting, identifying optimal strategies within the Pareto front. In both cases, we develop numerical algorithms allowing us to computationally assess the behavior of our models under various settings. Joint work with Y Saporito and Y Thamsten.

**[SAL] When a Ring meets a Lattice | João Dias (CIMA, Universidade de Évora)**

28 October 2024 2:00 pm - 3:00 pm

Seminar room, building VII

Abstract:

The rational numbers have been used to measure quantities since ancient times; however, their implementation in computer languages raises a significant problem: zero has no inverse. To address this issue, J. Bergstra and J. Tucker introduced an algebraic structure called a meadow, which allows for the inversion of zero.

In this talk, I will introduce meadows and their various classes, demonstrating that they correspond to labelled lattices, where the rings label the vertices. We will explore how concepts from ring theory, such as Artinian rings and decomposition theorems, can be adapted to this new context. Finally, I will present a connection between meadows and sheaves over a topological space, highlighting the implications of this relationship.

- J. Dias and B. Dinis. "Strolling through common meadows." Communications in Algebra, 2024, 1–28.

- J. Dias and B. Dinis. "Towards an enumeration of finite common meadows." International Journal of Algebra and Computation, 2024, 1-19.

- J. Dias, B. Dinis and P. Marques. Bridging Meadows and Sheaves. arXiv:2410.05921

**[SAL] Square root crystals and Grothendieck positivity | Eric Marberg (Hong Kong University of Science and Technology)**

4 November 2024 2:00 pm - 3:00 pm

Zoom link: https://videoconf-colibri.zoom.us/j/91864016501?pwd=J0qrDNWOva0DeM1XTOuUiDN3ToRd3b.1

The classical theory of type A crystals provides a graphical framework for proving Schur positivity results. In this talk we will discuss a new category of "square root crystals" (introduced implicitly in work of Yu) that can be used to establish instances of Grothendieck positivity. For example, Buch's combinatorial interpretation of the coefficients expanding products of symmetric Grothendieck functions has a simple description in terms of the tensor product for this category. We will also discuss some shifted analogues and applications to a conjectural formula of Cho-Ikeda for K-theoretic Schur P-functions.

**[SOR] Integrating public transport in sustainable last-mile delivery | Claudia Archetti (University of Brescia, Italy)**

20 November 2024 2:00 pm - 3:00 pm

Sala 1.4 - VII

Abstract: Integrating public transport in sustainable last-mile delivery

We consider a delivery system for last-mile deliveries in urban areas based on the use of Public Transport Service. The idea is to exploit the spare capacity of public transport means to transport parcels within urban areas, thus reducing externalities caused by commercial delivery vans. Specifically, the system is such that parcels are first transported from origins to drop-in stations on public vehicles itineraries. Then, they are transported through public vehicles to drop-out stations, from where they are delivered to destination by freighters using green vehicles. The system is known as Freight-On-Transit (FOT). We present the optimization problem related with and operational decisions, as well as ad-hoc solution methodologies and simulations on synthetic data.

SHORT BIO

ARCHETTI CLAUDIA

Claudia Archetti is Associate Professor of Operations Research at University of Brescia. From September 2021 to September 2024, she was Full Professor in Operations Research at ESSEC Business School in Paris. The main areas of the scientific activity are: models and algorithms for vehicle routing problems; mixed integer mathematical programming models for the minimization of the sum of inventory and transportation costs in logistic networks; exact and heuristic algorithms for supply-chain management; reoptimization of combinatorial optimization problems.

She is author of more than 100 papers in international journals. She is co-Editor in Chief of Networks. She was VIP3 of EURO, the Association of European Operational Research Societies, in charge of publications and communication.

**[SDataScience] Optimizing the Present and Future of Smart Electric Power Grids | Miguel F. Anjos (University of Edinburgh)**

27 November 2024 2:00 pm - 3:00 pm

Room 1.5, Building VII, NOVA FCT

**[SDataScience] Mechanistic mathematical models of harmful algal species | Ming Li (University of Maryland Center for Environmental Science)**

4 December 2024 2:00 pm - 3:00 pm

Room 1.5, Building VII, NOVA FCT

**[Mini-courseAn] Introduction to Dyadic Analysis | George Tephnadze (University of Georgia, Tbilisi, Georgia)**

10 December 2024 10:00 am - 12:00 pm

To announce.

**Title: **Introduction to Dyadic Analysis.

**Speaker**: George Tephnadze (University of Georgia, Tbilisi, Georgia).

**Lecture 1: **Tuesday, 10 December 2024, from 10:00 to 12:00.

**Lecture ****2****: **Thursday, 12 December 2024, from 10:00 to 12:00.

**Lecture ****3****: **Monday, 16 December 2024, from 10:00 to 12:00.

**Lecture ****4****: **Wednesday, 18 December 2024, from 10:00 to 12:00.

**Place: **To announce.

**Abstract: **The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.

Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.

This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

**Lecture 1: **We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

**Lecture 2: **We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

**Lecture 3: **We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

**Lecture 4: **We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.

This introduction to dyadic analysis is based on the following recent book (where complementary information and several open problems can be found in more general case):

L. E. Persson, G. Tephnadze and F. Weisz, Martingale Hardy Spaces and Summability of one-dimensional Vilenkin-Fourier Series, Birkhäuser/Springer, 2022.

*https://www.ug.edu.ge/en/persons/full/9177

**[Mini-courseAn] Introduction to Dyadic Analysis | George Tephnadze (University of Georgia, Tbilisi, Georgia)**

12 December 2024 10:00 am - 12:00 pm

To announce.

**Title: **Introduction to Dyadic Analysis.

**Speaker**: George Tephnadze (University of Georgia, Tbilisi, Georgia).

**Lecture 1: **Tuesday, 10 December 2024, from 10:00 to 12:00.

**Lecture ****2****: **Thursday, 12 December 2024, from 10:00 to 12:00.

**Lecture ****3****: **Monday, 16 December 2024, from 10:00 to 12:00.

**Lecture ****4****: **Wednesday, 18 December 2024, from 10:00 to 12:00.

**Place: **To announce.

**Abstract: **The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.

Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.

This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

**Lecture 1: **We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

**Lecture 2: **We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

**Lecture 3: **We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

**Lecture 4: **We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.

This introduction to dyadic analysis is based on the following recent book (where complementary information and several open problems can be found in more general case):

L. E. Persson, G. Tephnadze and F. Weisz, Martingale Hardy Spaces and Summability of one-dimensional Vilenkin-Fourier Series, Birkhäuser/Springer, 2022.

*__https://www.ug.edu.ge/en/persons/full/9177__

**[Mini-courseAn] Introduction to Dyadic Analysis | George Tephnadze (University of Georgia, Tbilisi, Georgia)**

16 December 2024 10:00 am - 12:00 pm

To announce.

**Title: **Introduction to Dyadic Analysis.

**Speaker**: George Tephnadze (University of Georgia, Tbilisi, Georgia).

**Lecture 1: **Tuesday, 10 December 2024, from 10:00 to 12:00.

**Lecture ****2****: **Thursday, 12 December 2024, from 10:00 to 12:00.

**Lecture ****3****: **Monday, 16 December 2024, from 10:00 to 12:00.

**Lecture ****4****: **Wednesday, 18 December 2024, from 10:00 to 12:00.

**Place: **To announce.

**Abstract: **The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.

Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.

This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

**Lecture 1: **We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

**Lecture 2: **We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

**Lecture 3: **We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

**Lecture 4: **We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.

This introduction to dyadic analysis is based on the following recent book (where complementary information and several open problems can be found in more general case):

L. E. Persson, G. Tephnadze and F. Weisz, Martingale Hardy Spaces and Summability of one-dimensional Vilenkin-Fourier Series, Birkhäuser/Springer, 2022.

18 December 2024 10:00 am - 12:00 pm

To announce.

**Title: **Introduction to Dyadic Analysis.

**Speaker**: George Tephnadze (University of Georgia, Tbilisi, Georgia).

**Lecture 1: **Tuesday, 10 December 2024, from 10:00 to 12:00.

**Lecture ****2****: **Thursday, 12 December 2024, from 10:00 to 12:00.

**Lecture ****3****: **Monday, 16 December 2024, from 10:00 to 12:00.

**Lecture ****4****: **Wednesday, 18 December 2024, from 10:00 to 12:00.

**Place: **To announce.

**Abstract: **The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.

Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.

This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

**Lecture 1: **We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

**Lecture 2: **We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

**Lecture 3: **We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

**Lecture 4: **We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.