Abstract: Many interesting examples of discrete integrable systems can be studied from the geometric point of view. In this talk we will consider two classes of examples of such systems: autonomous (QRT maps) and non-autonomous (discrete Painlevé equations). We introduce some geometric tools to study these systems, such as the blowup procedure to construct algebraic surfaces on which the mappings are regularized, linearization of the mapping on the Picard lattice of the surface and, for discrete Painlevé equations, the decomposition of the Picard lattice into complementary pairs of the surface and symmetry sub-lattices and construction of a birational representation of affine Weyl symmetry groups that gives a complete algebraic description of our non-linear dynamic. This talk is based on joint work with Stefan Carstea (Bucharest) and Tomoyuki Takenawa (Tokyo).
Bio: Anton Dzhamay is a Professor at the Department of Mathematical Sciences at the University of Northern Colorado, USA and also a Visiting Professor at the Beijing Institute of Mathematical Sciences and Applications (BIMSA). Anton got his undergraduate degree from Moscow Institute of Electronics and Mathematics and his PhD from Columbia University with Igor Krichever. His research interests are in the application of algebro-geometric methods in the theory of integrable systems. Recently his main focus has been the geometry behind Painlevé equations, both differential and discrete, as well as the effective use of algebro-geometric theory of Painlevé equations for various applications, particularly in Integrable Probability and Orthogonal Polynomials.
Abstract: The high-dimensional rank lasso (hdr lasso) model is an efficient approach to deal with high-dimensional data analysis. It was proposed as a tuning-free robust approach for the high-dimensional regression and was demonstrated to enjoy several statistical advantages over other approaches. The hdr lasso problem is essentially an $L_1$-regularized optimization problem whose loss function is Jaeckel's dispersion function with Wilcoxon scores. Due to the nondifferentiability of the above loss function, many classical algorithms for lasso-type problems are unable to solve this model. In this paper, we propose an adaptive-sieving-based algorithm to solve the hdr lasso problem. The proposed algorithm makes full use of the sparsity of the solution. In each iteration, a subproblem with the same form as the original model is solved, but in a much smaller size. Extensive numerical results demonstrate that the proposed algorithm (AS-PPA) is robust for different types of noises. Moreover, AS-PPA is also highly efficient, especially for the case of high-dimensional features, compared with other methods.
Abstract:
Customer picking behaviour plays an important role in retail inventory management. Standard inventory models usually distinguish between picking the newest items, i.e. Last-in-first-out (LIFO), or the oldest items first, i.e., First-in-first-out (FIFO). We analyze how LIFO and FIFO picking behaviour affects inventory management in retailing, and whether sustainability messages and price discounts can change customer picking behaviour to increase sales of earlier expiring items and reduce food waste in retailing. We conducted an online experiment where subjects chose between buying FIFO and LIFO using monetary and non-monetary incentives. Understanding how different customer types respond to incentives helps retailers to offer them only to customers who most likely respond with buying expiring items. We evaluate the effect of these findings on inventories using a periodic review model for perishable items with age-dependent lifetimes.
Abstract:
We introduce a new algorithm for solving Difference of Convex functions (DC) pro- gramming, called Boosted Difference of Convex functions Algorithm (BDCA). BDCA accelerates the convergence of the classical difference of convex functions algorithm (DCA) thanks to an additional line search step. We prove that any limit point of the BDCA iterative sequence is a critical point of the problem under consideration and that the corresponding objective value is monotonically de- creasing and convergent. The global convergence and convergence rate of the iterations are obtained under the Kurdyka–Lojasiewicz property. We provide applications and numerical experiments for a hard problem in biochemistry and two challenging problems in machine learning, demonstrating that BDCA outperforms DCA. For the biochemistry problem, BDCA was five times faster than DCA, for the Minimum Sum-of-Squares Clustering problem, BDCA was on average sixteen times faster than DCA, and for the Multidimensional Scaling problem, BDCA was three times faster than DCA.
Abstract:
The growth of offshore wind farms underscores the urgency for the industry to streamline operations and reduce inspection costs. Innovations in autonomous technology paired with digital advancements are paving the way for a more sustainable and secure inspection framework. This paper unveils a cutting-edge strategy that combines the capabilities of autonomous unmanned surface vessels (USVs) with drone swarms, also known as unmanned aerial vehicles (UAVs), to carry out offshore wind turbine inspections. This innovative solution is particularly aimed at overcoming the drones' limited battery capacity, which significantly limits their ability to sustain flight and maintain communication during extensive missions. Autonomous USVs are equipped with specialised docking and recharging stations, ensuring drones can be re-energised mid-mission. The operational dynamic, where drones require a substantial 90-minute recharge after around 30 minutes of activity, poses a unique challenge in keeping the inspection workflow uninterrupted. To address this, we have developed a deterministic optimisation model and a multi-stage Bees Algorithm, designed to streamline the deployment and operational scheduling of drone swarms and USVs for turbine inspections. Our analysis explores the efficacy of this synergistic model and the innovative metaheuristic approach in optimising the logistical and operational framework for offshore wind farm inspections, highlighting significant advancements in routing and scheduling efficiency.
Abstract
We seek to derive and implement models that can accurately predict the behaviour of phase-changing electrode materials such as lithium iron phosphate (LFP) and graphite. This includes predicting voltage hysteresis during charge/discharge cycles and distinctive regimes of phase separation on both micro and macro scales. Typically, phase change in nano-particles such as LFP can be accurately predicted using a Cahn-Hilliard model, however, its computational cost makes it inapplicable on the scale of an entire electrode consisting of over 10^5 individual particles. We derive a 0D reduction of the electrochemical potential of a single particle in quasi-equilibrium from analysing the Chan-Hilliard model and apply it in a multiscale model to simulate an ensemble of interacting particles in a working electrode, successfully displaying hysteresis and different phase change regimes that are observed in experiments. Models from this work are currently being implemented in an open-source battery simulation package written in Python (PyBaMM).
Abstract: We propose a variation of the forward--backward splitting method for solving structured monotone inclusions and nonexpansive fixed-point problems. Our method integrates past iterates and two so-called deviation vectors into the update equations. These deviation vectors bring flexibility to the algorithm and can be chosen arbitrarily as long as they together satisfy a norm condition. We present special cases or our algorithm where the deviation vectors, selected as predetermined linear combinations of previous iterates, always meet the norm condition. The resulting algorithms significantly outperform previous methods on a basic fixed-point problem problem stemming from minimax optimization.
Bio: Pontus Giselsson is an Associate Professor at the Department of Automatic Control at Lund University, Sweden. His current research interests include mathematical optimization and its applications in, e.g., control, machine learning, statistical estimation, and signal processing. He received an MSc degree from Lund University in 2006 and a PhD degree from Lund University in 2012. During 2013 and 2014, he was a postdoc at Stanford University and has been with with Lund University since 2015.
Abstract:
I will present how the mathematics of stochastic processes can be used to model the very early universe. Our best current model is spacetime itself was expanding exponentially at early times - a process called Inflation. This explains the observed homogeneity, flatness, and large-scale structure of our universe. The latter is seeded by microscopic quantum fluctuations, which are grown to macroscopic scales by the rapid expansion. In the standard approach, this is calculated using linear perturbation theory. But in this talk I will explain how tools from stochastic calculus can be used to go beyond linear theory. I will focus on presenting the mathematics of this complex process and give a review of recent progress in the field.
Abstract:
The recent quantum information revolution stimulated applications of the mathematical formalism and methodology of quantum theory outside of physics: to cognition, psychology, decision making, and social science. Quantum probability and information can be applied to these areas to model statistical data exhibiting quantum-like properties, as interference of probabilities - as violation of the formula of total probability, the order, conjunction, disjunction, and response replicability effects, the violation of the Bell inequalities. Such quantum-like modeling should not be mixed with biophysics, study of genuine physical processes in biosystems, including the brain. The essence of applicability of quantum-like modeling is not systems' size, but the rules of information processing, so even macro-systems can work in some regimes as quantum information processors.
The second part of the talk is devoted to the special application of quantum-like modeling to social processes - the social laser theory. During the last years our society was permanently disturbed by the coherent information waves of high amplitudes. These are waves of huge social energy. Often, they are of the destructive character, a kind of information tsunami. But they can carry as well positive improvements in the human society, as waves of decision making matching rational recommendations of societal institutes. The main distinguishing features of these waves are their high amplitude, coherence (homogeneous character of social actions generated by them), and short time needed for their generation and relaxation.
We show that such social phenomenon can be modelled on the basis of the recently developed social laser theory. This theory can be used to model stimulated amplification of coherent social actions.
''Actions'' are treated very generally, from mass protests to votes and other collective decisions, as, e.g., acceptance (often unconscious) of some societal recommendations. We point to the main distinguishing features of the modern society simplifying social lasing: a) transformation of humans into social atoms - loss of individuality and increase of indistinguishability; b) generation by mass-media of powerful information fields leading to information overload of social atoms; c) creation of powerful social resonators based on internet Echo Chambers Functioning of internet based social resonators leads to increase of the power of the quantum information field as well as its coherence.
Abstract: The Julia programming language is a dynamic programming language, with a focus on productivity and performance. It's finding increasing adoption in numerical and scientific computing, data processing and analytics, differentiable programming and scientific machine learning. In this talk we will go through some of Julia's main features, and applications.
Abstract: Controlling the polarization of photons is an essential feature for several applications in quantum optics and technologies. In this respect, it is essential to measure such a parameter with the best precision possible. Here we employ novel interferometric techniques to measure the difference in the polarizations of two photons based on two photon interference. We use statistical estimation theory to compare the efficiency of different experimental setups and verify for each of them what are the conditions for saturating the Cramer-Rao bound, paving the way to future application in quantum information processes and technologies.
Marianna Cerasuolo (1), Andrew Burbanks (2), Roberto Ronca (3), Leo D Turner (2)
(1) University of Sussex, United Kingdom. (2) University of Portsmouth, United Kingdom. (3) University of Brescia, Italy.
Abstract:
Androgen deprivation therapy’s ability to reduce tumour growth represents a milestone in prostate cancer treatment. Nonetheless, most patients eventually become refractory and develop castration-resistant prostate cancer (CRPC). Second-generation drugs and their combination have been recently approved for the treatment of CRPC. However, cases of tumour resistance to these new drugs have now been reported. In the last few years, many mathematical models have been proposed to describe the dynamics of prostate cancer under treatment. So far, one of the significant challenges has been the development of mathematical models that could represent experiments in in vivo conditions (experiments on individuals) and, therefore, be suitable for clinical applications while being mathematically tractable.
In this talk, I will present a comprehensive study of the phenomena of castration and drug resistance in prostate cancer. I will show how, through the integration of experimental data, statistical analysis and mathematical and computational approaches, it was possible to gain insights into the reasons behind resistance and potential therapeutic strategies to overcome it. Two models will be proposed: a nonlinear distributed-delay dynamical system that explores neuroendocrine transdifferentiation in human prostate cancer in vivo under androgen deprivation therapy [1] and a hybrid cellular automaton with stochastic elements to represent multiple drug therapies [2].
The analytical and numerical study of the first dynamical system showed how the choice of the delay distribution is critical in defining the system’s dynamics and determining the conditions for the onset of oscillations following a Hopf bifurcation. On the other hand, through the computational analysis of the hybrid model, it was possible to investigate the spatial behaviour of tumour cells, the effectiveness of multiple drug therapies on prostate cancer growth, and to identify the best drug combination strategies and treatment schedules to achieve the extinction of cancer cells and avoid metastasis formation. The model revealed that combination and alternating therapies can delay the onset of drug resistance and, in suitable scenarios, can eliminate the disease.
The presented mathematical systems incorporate phenomena previously reported in the literature [3,4,5] and verified in the laboratory, such as cell phenotype switching due to drug resistance acquisition and the micro-environment dynamics’ effect on the tumour cells’ necrosis and apoptosis.
References:
[1] Turner, L., Burbanks, A., & Cerasuolo, M. (2021). PCa dynamics with neuroendocrine differentiation and distributed delay. Mathematical Biosciences and Engineering, 18(6), 8577–8602.
[2] Burbanks A, Cerasuolo M, Ronca R, Turner L, 2023. A hybrid spatiotemporal model of PCa dynamics and insights into optimal therapeutic strategies. Mathematical Biosciences, 355, 108940.
[3] J. Baez, Y. Kuang, Mathematical models of androgen resistance in prostate cancer patients under intermittent androgen suppression therapy, Appl. Sci., 6 (2016), 352.
[4] A. Anderson, 2005. A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion, Math. Med. Biol. 22, 163-186.
[5] M. Cerasuolo, F. Maccarinelli, D. Coltrini, A. Mahmoud, V. Marolda, G. Ghedini, S. Rezzola, A. Giacomini, L. Triggiani, M. Kostrzewa, R. Verde, D. Paris, D. Melck, M. Presta, A. Ligresti, R. Ronca, 2020. Modeling acquired resistance to the second-generation androgen receptor antagonist enzalutamide in the tramp model of prostate cancer, Cancer Res. 80 (7), 1564–157.
Abstract: Quantum sensors enable the measurement of physical quantities with far better accuracy than it is possible with classical technologies. The single-parameter estimation has been extensively investigated in earlier studies but the multi-parameter estimation is still to be explored. We aim to achieve the ultimate quantum sensitivity given by Heisenberg-scaling precision δφ = O(1/N), where N is the average number of photons in the probe, to estimate multiple unknown physical parameters in an optical distributed network. In particular, we employ as probes scalable non-classical sources robust to the decoherence and experimentally feasible, such as squeezed light to simultaneously estimate two parameters to the Heisenberg limited sensitivity.
Abstract: The deformation of random symmetric matrix ensembles underpins a semi-discrete integrable hierarchy structure named the Pfaff lattice. We study the case for which the weight function in the joint probability density function of the ensemble is even, with focus on the thermodynamic limit of the field variables populating the lattice. At the leading order a system of infinitely many PDEs emerges, that can be recast in the form of a new integrable hydrodynamic chain.
Abstract: Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This work focuses on Inverse Optimal Transport (iOT), the problem of inferring the ground cost from samples drawn from a coupling that solves an eOT problem. It is a relevant problem that can be used to infer unobserved/missing links, and to obtain meaningful information about the structure of the ground cost yielding the pairing. On one side, iOT benefits from convexity, but on the other side, being ill-posed, it requires regularization to handle the sampling noise. This work presents a study of l1 regularization to model for instance Euclidean costs with sparse interactions between features. Specifically, we derive a sufficient condition for the robust recovery of the sparsity of the ground cost that can be seen as a generalization of the Lasso’s celebrated ``Irrepresentability Condition’’. To provide additional insight into this condition, we consider the Gaussian case. We show that as the entropic penalty varies, the iOT problem interpolates between a graphical Lasso and a classical Lasso, thereby establishing a connection between iOT and graph estimation. This is joint work with Francisco Andrade and Gabriel Peyré.
Bio: Clarice Poon is an associate professor in the Mathematical Institute at the University of Warwick. She received her PhD in applied mathematics from the University of Cambridge and her undergraduate degree in Mathematics and Computer Science from the University of Oxford. Her research interests include compressed sensing, inverse problems on measures and optimisation for imaging problems.