### New talk in the Proof Mining Seminar

Morenikeji Neri (University of Bath) will give on
Wednesday, July 31, at 16:00 the talk
**Proof mining and probability**
in the Proof Mining Seminar.

Morenikeji Neri (University of Bath) will give on
Wednesday, July 31, at 16:00 the talk
**Proof mining and probability**
in the Proof Mining Seminar.

Mihai Prunescu published (in collaboration with Lorenzo Sauras-Altuzarra)
the preprint **On the representation of number-theoretic functions by arithmetic terms**
on arXiv.

Laurențiu Leuștean published (in collaboration with Paulo Firmino)
the paper **Quantitative asymptotic regularity of the VAM iteration with error
terms for accretive operators in Banach spaces** in Zeitschrift für Analysis und ihre Anwendungen.

The Research Center for Logic, Optimization and Security (LOS) was founded in October 2020 by
Laurenţiu Leuştean (head), Paul Irofti and Andrei Pătraşcu.

Our main objective is to stimulate interdisciplinary research in the fields of logic,
optimization and security. We are interested both in fundamental research as well as in
industrial applications. We focus on proof mining and applications to optimization, ergodic theory
and nonlinear analysis, convex optimization for machine learning, signal processing and
matrix factorization (dictionary learning), security, anomaly detection and anti-money laundry.

Contact

Hall 317, Faculty of Mathematics and Computer Science,

Academiei 14, 010014 Bucharest, Romania

Email: los@fmi.unibuc.ro

The project PROFET aims at developing and implementing a better solution compared to the existing ones regarding the precise positioning of a satellite onto its orbit. The efficiency of our approach comes from the low frequency of interaction between the space object and the GNSS (Global Navigation Satellite System) network. To achieve this, the definition of mission requirements, altogether with data retrieval from the orbital satellite is needed. The successful design of the estimation algorithms will be followed by the definition of the hardware requirements and the design of an electronic module, the estimation software being implemented at the firmware level, afterwards.

NetAlert aims to create a hardware-software sensor solution for detecting anomalies in computer networks
based on the monitoring and analysis of data packets.
The network-mounted sensor will provide real-time alerts on abnormal traffic behaviors
using two complementary approaches:

(i) static analysis based on rules and behavioral patterns;

(ii) machine learning (ML) analysis without prior expert knowledge.

The main goal of this project, called DDNET, is to adapt and propose
new dictionary learning methods for solving untractable
fault detection and isolation problems found in distribution networks.
Given a large dataset of sensor measurements from the distribution network,
the dictionary learning algorithms should be able to produce the subset
of network nodes where faults exist.

Graphomaly (287PED/2020)

The proposed project, called Graphomaly, aims to create a
Python software package for anomaly detection in graphs
that model financial transactions,
with the purpose of discovering fraudulent behavior like money laundering,
illegal networks, tax evasion, scams, etc.
Such a toolbox is necessary in banks, where fraud detection departments
still use mostly human experts.

StOpAnomaly (143PD/2020)

StOpAnomaly aims to create, analyze and implement numerical optimization algorithms for large-scale optimization focusing on robust anomaly detection models based on decomposition and one-class classification. The research will be directed towards development of a toolbox containing scalable stochastic algorithms that can be used to detect several classes of anomalies in noisy large datasets.

Scientific seminars organized by LOS members

The working seminar of the LOS research center.

The seminar features talks on mathematical logic, philosophical logic and logical aspects of computer science.

The seminar presents recent results on proof mining.

- M. Prunescu, L. Sauras-Altuzarra, On the representation of number-theoretic functions by arithmetic terms, arXiv:2405.04083 [math.LO] (2024).
- P. Firmino, L. Leuștean, Quantitative asymptotic regularity of the VAM
iteration with error terms for accretive operators in Banach spaces,
Zeitschrift für Analysis und ihre Anwendungen (2024)

DOI: https://doi.org/10.4171/ZAA/1772 - H. Cheval, Quantitative metastability of the Tikhonov-Mann iteration for countable families of mappings, arXiv:2406.03429 [math.OC] (2024).
- M. Prunescu, On other two representations of the C-recursive integer sequences by terms in modular arithmetic, arXiv:2406.06436 [math.NT] (2024).
- H. Cheval, L. Leuştean, Linear rates of asymptotic regularity
for Halpern-type iterations, Mathematics of Computation (2024)

DOI: https://doi.org/10.1090/mcom/3991 - L. Leuştean, P. Pinto, Rates of asymptotic
regularity for the alternating Halpern-Mann iteration, Optimization Letters 18:529-543 (2024).

DOI:10.1007/s11590-023-02002-y - M. Prunescu, L. Sauras-Altuzarra, On the representation of C-recursive integer sequences by arithmetic terms, arXiv:2405.04083 [math.LO] (2024).
- P. Irofti, I.A. Hîji, A. Pătrașcu, N. Cleju Fusing Dictionary Learning and Support Vector Machines for Unsupervised Anomaly Detection, arXiv:2404.04064 [cs.LG] (2024).
- A. Pătrașcu, C. Rusu, P. Irofti Learning Explicitly Conditioned Sparsifying Transforms, arXiv:2403.03168 [math.NA] (2024).
- M. Prunescu, L. Sauras-Altuzarra
An arithmetic term for the factorial function,
Examples and Counterexamples, 5:100136 (2023).

DOI:10.1016/j.exco.2024.100136 - L. Romero-Ben, P. Irofti, F. Stoican, V. Puig Nodal Hydraulic Head Estimation through Unscented Kalman Filter for Data-driven Leak Localization in Water Networks, arXiv:2311.15875 [eess.SY] (2023).
- P. Irofti, L. Romero-Ben, F. Stoican, V. Puig Learning Dictionaries from Physical-Based
Interpolation for Water Network Leak Localization,
IEEE Transactions on Control Systems Technology (2023).

DOI: 10.1109/TCST.2023.3329696 - P. Irofti, Pinky: A Modern Malware-oriented Dynamic Information Retrieval Tool,
International Conference on Information Technology and Communications Security (SecITC 2023), Springer, 65-78 (2023).

DOI:10.1007/978-3-031-52947-4_6 - A. Stancu, P. Irofti, I. Leuștean, OpenBSD formal driver verification
with SeL4,
International Conference on Information Technology and Communications Security (SecITC 2023), Springer, 144-156 (2023).

DOI:10.1007/978-3-031-52947-4_11 - R. Bălucea, P. Irofti, Software Mitigation of RISC-V Spectre Attacks,
International Conference on Information Technology and Communications Security (SecITC 2023), Springer, 51-64 (2023).

DOI:10.1007/978-3-031-52947-4_5 - L. Păunescu, A. Sipoş, A
proof-theoretic metatheorem for tracial von Neumann algebras, Mathematical Logic Quarterly, 69(1):63-76 (2023),

DOI: 10.1002/malq.202200048 - H. Cheval, Rates of asymptotic regularity of the Tikhonov-Mann iteration for families of mappings, arXiv:2304.11366 [math.OC] (2023).
- H. Cheval, U. Kohlenbach, L. Leuştean,
On modified Halpern and Tikhonov-Mann iterations, Journal of Optimization Theory and Applications 197:233-251 (2023).

DOI: 10.1007/s10957-023-02192-6 - A. Sipoş, The computational content of super strongly nonexpansive mappings and uniformly monotone operators, arXiv:2303.02768 [math.OC] (2023).
- S.S. Mihai, F. Stoican, B.D. Ciubotaru,
On the link between explicit MPC and the face lattice of the lifted feasible domain,
18th IFAC Workshop on Control Applications of Optimization (CAO22), 308-313 (2022).

DOI: 10.1016/j.ifacol.2022.09.042 - T.G. Nicu, F. Stoican, I. Prodan,
Polyhedral potential field constructions for obstacle avoidance in a receding horizon formulation,
18th IFAC Workshop on Control Applications of Optimization (CAO22), 254-259 (2022).

DOI: 10.1016/j.ifacol.2022.09.033 - A. Sipoş, Revisiting jointly firmly nonexpansive
families of mappings, Optimization, 71:3819-3834 (2022).

DOI: 10.1080/02331934.2021.1915312 - M. Prunescu, Symmetries in the Pascal triangle: $p$-adic valuation, sign-reduction modulo $p$ and the last non-zero digit, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 65 (113):431-447 (2022).
- A. Sipoş, On quantitative metastability for accretive operators , arXiv:2210.11131 [math.FA] (2022).
- L. Păunescu, A. Sipoş, A proof-theoretic metatheorem for tracial von Neumann algebras, arXiv:2209.01797 [math.LO] (2022).
- A. Pătraşcu, P. Irofti, On
finite termination of an inexact Proximal Point algorithm,
Applied Mathematics Letters (2022)

DOI: 10.1016/j.aml.2022.108348. - A. Sipoş, Abstract strongly convergent variants of the proximal point algorithm
, Computational Optimization and Applications 83:349-380 (2022),

DOI: 10.1007/s10589-022-00397-5 - A. Sipoş,
On extracting variable Herbrand disjunctions,
Studia Logica 110:1115–1134, (2022),

DOI: 10.1007/s11225-022-09990-5 - P. Irofti, L. Romero-Ben, F. Stoican, V. Puig, Data-driven Leak Localization in Water Distribution Networks via Dictionary Learning and Graph-based Interpolation, in Proceedings of the 2022 6th IEEE Conference on Control Technology and Applications (CCTA22) (2022)
- P. Irofti, A. Pătrașcu, A.I Hîji, Unsupervised Abnormal Traffic Detection through Topological Flow Analysis, in Proceedings of the 14th International Conference on Communications (COMM2022) (2022)
- A. Sipoş, Quantitative inconsistent feasibility
for averaged mappings, Optimization Letters 16:1915–1925 (2022),

DOI: 10.1007/s11590-021-01812-2 - H. Cheval, L. Leuştean, Quadratic rates of
asymptotic regularity for
the Tikhonov-Mann iteration, Optimization Methods and Software (2022),

DOI: 10.1080/10556788.2022.2060974 - P. Irofti, C. Rusu, A. Pătraşcu,
Dictionary Learning with Uniform Sparse Representations
for Anomaly Detection, in Proceedings of 2022 IEEE International
Conference on Acoustics, Speech and Signal Processing (ICASSP 2022),
IEEE Computer Society, 3378-3382
(2022),

DOI: 10.1109/ICASSP43922.2022.9747365 - C. Rusu, C. Rosasco, Fast approximation of
orthogonal matrices and application to PCA, Signal Processing 194:108451 (2022),

DOI: 10.1016/j.sigpro.2021.108451 - C. Rusu, An iterative Jacobi-like algorithm to compute a few sparse eigenvalue-eigenvector pairs, arXiv:2105.14642 [math.NA] (2021)
- A. Pătraşcu, P. Irofti, Computational complexity of Inexact Proximal Point Algorithm for Convex Optimization under Holderian Growth, arXiv:2108.04482 [cs.LG] (2021)
- C. Rusu, An iterative coordinate descent algorithm
to compute sparse low-rank approximations,
IEEE Signal Processing Letters (2021),

DOI: 10.1109/LSP.2021.3132276 - A. Sipoş, Bounds on strong unicity for
Chebyshev approximation with bounded coefficients, Mathematische Nachrichten 294:2425–2440 (2021),

DOI: 10.1002/mana.201900439 - C. Rusu, P. Irofti, Efficient and Parallel Separable Dictionary Learning, in Proceedings of the IEEE 27th International Conference on Parallel and Distributed Systems (ICPADS 2021), IEEE Computer Society, 1-6 (2021)
- I. Leuştean, B. Macovei, DELP: Dynamic Epistemic Logic for Security Protocols, in Proceedings of the 23rd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2021), 275-282 (2021)
- A. Sipoş, A quantitative multiparameter
mean ergodic theorem, Pacific Journal of Mathematics 314:209 - 218 (2021),

DOI: 10.2140/pjm.2021.314.209 - C. Rusu, L. Rosasco,
Constructing fast approximate eigenspaces with application to the fast graph Fourier transforms,
IEEE Transactions on Signal Processing (2021),

DOI: 10.1109/TSP.2021.3107629 - A. Sipoş,
Construction of Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Convex Hyperbolic Spaces
, Numerical Functional Analysis and Optimization 42:696-711 (2021),

DOI: 10.1080/01630563.2021.1924780 - A. Sipoş, Rates of metastability for iterations
on the unit interval, Journal of Mathematical Analysis and Applications 502:125235 (2021),

DOI: 10.1016/j.jmaa.2021.125235 - L. Leuştean, P. Pinto,
Quantitative results on a Halpern-type proximal point algorithm,
Computational Optimization and Applications 79:101–125 (2021),

DOI: 10.1007/s10589-021-00263-w - A. Pătraşcu, P. Irofti,
Stochastic proximal splitting algorithm for composite minimization,
Optimization Letters 15:2255–2273 (2021),

DOI: 10.1007/s11590-021-01702-7