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52      <div id="particles-js">
53  <div class="header">
54      <h1>
55        <span class="site-title">Fabio Durastante</span>
56        <span class="site-description">Associate Professor</span>
57      </h1>
58      <div class="header-icons">
59        <a aria-label="Send email" href="mailto:[email protected]"><i class="icon fa fa-envelope"></i></a>
60        <a aria-label="My Twitter" href="https://twitter.com/CirdansHome" targe="_blank"><i class="icon fa fa-twitter"></i></a>
61        <a aria-label="My LinkedIn" target="_blank" href="https://www.linkedin.com/in/fdurastante/"><i class="icon fa fa-linkedin-square" aria-hidden="true"></i></a>
62        <a aria-label="My Github" target="_blank" href="https://github.com/Cirdans-Home"><i class="icon fa fa-github-alt" aria-hidden="true"></i></a>
63        <a aria-label="My ResearchGate" target="_blank" href="https://www.researchgate.net/profile/Fabio_Durastante2"><i class="icon fab fa-researchgate" aria-hidden="true"></i></a>
64        <a aria-label="My GoogleScholar" target="_blank" href="https://scholar.google.it/citations?user=sB3fLcMAAAAJ&hl=it"><i class="icon fab fa-google" aria-hidden="true"></i></a>
65        <a aria-label="My Orcid" target="_blank" href="https://orcid.org/0000-0002-1412-8289"><i class="icon fab fa-orcid" aria-hidden="true"></i></a>
66      </div>
67      <div class="header-links">
68        <a class="link" href="/research.html">Research</a>
69        <a class="link" href="/projects.html">Projects</a>
70        <a class="link" href="/conferences.html">Conferences</a>
71        <a class="link" href="/code.html">Code</a>
72        <a class="link" href="/teaching.html">Teaching</a>
73        <a class="link" href="/students.html">Students&#38;Theses</a>
74      </div>
75  </div>
76  <a class="down" href="#about" data-scroll><i class="icon fa fa-chevron-down" aria-hidden="true"></i></a>
77</div>
78
79      <section id="about">
80      <div class="standard-page" style="text-align: justify; text-justify: inter-word;">
81        <h1>Research</h1>
82
83My research activities are divided into different strands and projects.
84The publications are reported by subject area and project in descending
85temporal order.<br>
86
87The same information can be found on either my <a href="https://scholar.google.it/citations?user=sB3fLcMAAAAJ&hl=it"
88target="_blank"><i class="fab fa-google"> Google Scholar Profile</i></a>, my
89<a href="https://www.researchgate.net/profile/Fabio_Durastante2" target="_blank">
90  <i class="fab fa-researchgate"> ResearchGate</i></a>, or my
91<a href="https://orcid.org/0000-0002-1412-8289" target="_blank"><i class="fab fa-orcid">
92  Orcid</i></a> profile.<br><br>
93
94
95Solving Linear Algebra problems is a core task in pretty much every Scientific
96challenge, from the numerical solution of partial differential equations to the
97new problems arising in the analysis of larger and larger sets of data. Moreover,
98we are fastly moving towards the use of exascale-enabled HPC platforms, thus we
99need to be capable of pushing our algorithms (and codes) to work efficiently in
100this environment. This first research line deals with this type of issue, and
101more specifically with the task of solving linear systems of equations,
102$$ A \mathbf{x} = \mathbf{b}, \qquad A \in \mathbb{R}^{N \times N}, \; \mathbf{x},\mathbf{b} \in \mathbb{R}^{N}, $$
103in which $A$ is a <em>large</em>, $N \geq 10^9$, and <em>sparse</em>,
104number on non-zero entries proportional to $N$, matrix. The key instruments are
105here <b>Krylov Subspace Methods</b>, <b>Geometric</b> and <b>Algebraic Multigrid</b>
106preconditioners, and the application of update strategies to deal with more than
107one linear system.
108<table style="width:100%">
109  <colgroup>
110   <col span="1" style="width: 30%;">
111   <col span="1" style="width: 70%;">
112 </colgroup>
113 <tr>
114   <td style="text-align: center">Preconditioning for large and sparse linear systems</td>
115   <td><ul class="fa-ul">
116     <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span>
117      <strong>Bucci, A.</strong>; <strong>Durastante, F.</strong>;
118      An Equivalence result for sketched Anderson Acceleration and sketched GMRES
119      <em>Submitted</em> 2026.
120       <p style="text-align: right;"><a href="https://arxiv.org/abs/2607.04904" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p>
121
122     </li>
123     <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span>
124     <strong>Lombardo, L.</strong>; <strong>Durastante, F.</strong>;
125     Evaluating Rust for Sparse Matrix Kernels in Scientific Computing
126     <em>Submitted</em> (2026).
127     <p style="text-align: right;"><a href="https://arxiv.org/abs/2606.19213" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p>
128
129     </li>
130     <li><span class="fa-li"><i class="fa-regular fa-square"></i></span>
131     <strong>Durastante, F.</strong>; <strong>Mazza, M.</strong>;
132     Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods
133     <em>Springer INdAM Series (SINDAMS, volume XX)</em>. <strong>Accepted</strong> (2026). 
134     <p style="text-align: right;"><a href="http://arxiv.org/abs/2511.21597" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p>
135
136     </li>
137    <li><span class="fa-li"><i class="fa-regular fa-square"></i></span>
138    <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>;
139    <strong>Filippone, S.</strong>. Parallel matching-based AMG preconditioners 
140    for elliptic equations discretized by IgA. 
141    <em>Springer INdAM Series (SINDAMS, volume XX)</em>. <strong>Accepted</strong> (2026).  
142  <p style="text-align: right;"><a href="http://arxiv.org/abs/2511.21268" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p>
143  
144  </li>
145  <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
146  <strong>Boella, E.</strong>; <strong>Angersbach, R.</strong>; <strong>Anton, D.</strong>; <strong>Agullo, E.</strong>;
147  <strong>Audit, E.</strong>; <strong>Avila, M.</strong>; <strong>Bernaschi, M.</strong>; <strong>Buonocore, F.</strong>;
148  <strong>Buttari, A.</strong>; <strong>Calosso, B.</strong>; <strong>Carrozzo, M.G.</strong>; <strong>Catillo, M.</strong>; <strong>Celestini, A.</strong>;
149  <strong>Celino, M.</strong>; <strong>Conrads, C.</strong>; <strong>D’Ambra, P.</strong>; <strong>Di Napoli, E.</strong>;
150  <strong>Durastante, F.</strong>; <strong>Fahad, M.</strong>; <strong>Filippone, S.</strong>; <strong>Giraud, L.</strong>;
151  <strong>Giusepponi, S.</strong>; <strong>Grandgirard, V.</strong>; <strong>Gregori, D.</strong>; <strong>Koestler, H.</strong>
152  <strong>Kollet, S.</strong>, <strong>Kruse, C.</strong>, <strong>Majone, B.</strong>, <strong>Marait, G.</strong>, <strong>Mayo-García, R.</strong>,
153  <strong>Moríñigo, J.-A-</strong>; <strong>Nakov, S.</strong>; <strong>Obrejan, K.</strong>; <strong>Owen, H.</strong>;
154  <strong>Pecchia, A.</strong>; <strong>Robeyns, M.</strong>; <strong>Rocco, R.</strong>; <strong>Schottenhamml, H.</strong>; 
155  <strong>Anciaux Sedrakian, A.</strong>; <strong>Suffa, P.</strong>; <strong>Vacek, P.</strong>. 2026. The
156  Energy-Oriented Centre of Excellence: Invited Paper. In Proceedings of the 23rd ACM International Conference on Computing Frontiers (CF Companion’26), 
157  May 19-21, 2026, Catania, Italy. ACM, New York, NY, USA, 9 pages.
158    <a href="/bibtex/Boella2026.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
159    <a href="/papers/EoCoeACM.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
160    <a href="https://dl.acm.org/doi/10.1145/3801488.3806243" target="_blank">Open access</a>.
161    </li>
162    <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
163    <strong>Durastante, F.</strong>; <strong>Mazza, M.</strong>;
164    Stage-Parallel Implicit Runge-Kutta methods via low-rank matrix equation corrections.
165    J Sci Comput <strong>107</strong>, (2026) no. 4 .  
166    <a href="/bibtex/Durastante2026.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
167    <a href="/papers/JSC2026.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
168    <a href="https://github.com/Cirdans-Home/SP_IRK.jl" target="_blank"><i class="fa-solid fa-code"></i></a>
169    <a href="https://doi.org/10.1007/s10915-026-03185-z" target="_blank">Open access</a>.
170    </li>
171    <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
172    <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>;
173    <strong>Filippone, S.</strong>.
174    PSCToolkit: Solving Sparse Linear Systems with a Large Number of GPUs.
175    <em>Emerging Technologies in Computational Sciences for Industry, Sustainability and Innovation. M2P 2023.</em>
176    Lect. Notes Comput. Sci. Eng., <strong>146</strong>. Springer, Cham. (2025).
177    <a href="/bibtex/Dambra2025b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
178     </li>
179     </li>
180     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
181     <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>;
182     <strong>Filippone, S.</strong>; <strong>Massei, S.</strong>;
183     <strong>Thomas, S.</strong>; Optimal Polynomial Smoothers for Parallel AMG.
184     <em>Numer Algor</em> (2025). 
185     <a href="/bibtex/Dambra2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
186     <a href="https://rdcu.be/eqfit" target="_blank">Read Online</a>
187     </li>
188     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
189     <strong>Owen, H.</strong>; <strong>Lehmkuhl, O.</strong>;
190     <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>;
191     <strong>Filippone, S.</strong>; Alya towards Exascale: Algorithmic Scalability
192     using PSCToolkit. <em>J. Supercomput</em> (2024).
193     <a href="/bibtex/Owen2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
194     <a href="/papers/JSC2024.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
195     <a href="https://doi.org/10.1007/s11227-024-05989-y" target="_blank">Open access</a>
196     </li>
197     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
198      <strong>Bertaccini, D.</strong>; <strong>D'Ambra, P.</strong>;
199      <strong>Durastante, F.</strong>; <strong>Filippone, S.</strong>;
200      Why diffusion-based preconditioning of Richards equation works: spectral
201      analysis and computational experiments at very large scale. (2023).
202      <em>Numer. Linear Algebra Appl.</em>; e2523.
203      <a href="/bibtex/Bertaccini2023.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
204      <a href="/papers/NLAA2023.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
205      <a href="https://doi.org/10.1002/nla.2523" target="_blank">Open access</a>
206     </li>
207     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
208       <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>;
209       <strong>Filippone, S.</strong>; <strong>Zikatanov, L.</strong>.
210       Automatic coarsening in Algebraic Multigrid utilizing quality measures
211       for matching-based aggregations. <i>Comput. Math. Appl.</i> <strong>144</strong> (2023),
212       290-305. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4615364" target="_blank">
213       <strong>MR4615364</strong></a>
214       <a href="/bibtex/DAmbra2023c.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
215       <a href="/papers/CAMWA2023.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
216       <a href="https://doi.org/10.1016/j.camwa.2023.06.026" target="_blank">Open access</a>
217     </li>
218     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
219       <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>;
220       <strong>Ferdous, S.M.</strong>; <strong>Filippone, S.</strong>;
221       <strong>Halappanavar, M.</strong>; <strong>Pothen A.</strong>.
222       AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective
223       Graph Matching. (2023). <em>31st Euromicro International Conference on Parallel,
224       Distributed and Network-Based Processing (PDP), Naples, Italy, 2023</em>, pp. 59-67.
225       <a href="/bibtex/Dambra2023b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
226     </li>
227     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
228     <strong>P. D'Ambra</strong>; <strong>F. Durastante</strong>;
229     <strong>S. Filippone</strong>; Parallel Sparse Computation Toolkit.
230     <em>Software Impacts</em> <strong>15</strong> (2023), no. 100463.
231     <a href="/bibtex/Dambra2023.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
232     <a href="/papers/SIMPAC2023.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
233     <a href="https://doi.org/10.1016/j.simpa.2022.100463" target="_blank">Open Access</a>.
234     </li>
235     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
236       <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>;
237       <strong>Filippone, S.</strong>.
238       AMG Preconditioners for Linear Solvers towards Extreme Scale.
239        <em>SIAM J. Sci. Comput.</em> <strong> 43 </strong> (2021),
240        no. 5, S679-S703.
241        <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4331965" target="_blank">
242          <strong>MR4331965</strong></a>
243        <a href="/bibtex/Dambra2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
244     </li>
245     <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
246         <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>.
247         Iterative methods and preconditioning for large and sparse linear systems
248         with applications. Monographs and Research Notes in Mathematics.
249         <em>CRC Press, Boca Raton, FL,</em>  2018. xviii+353 pp.
250         ISBN: 978-1-4987-6416-2
251         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3793630"
252         target="_blank"><strong>MR3793630</strong></a>
253         <a href="/bibtex/Bertaccini2018b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
254       </li>
255       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
256         <strong>Bertaccini, D.</strong>; <strong>Donatelli, M.</strong>;
257         <strong>Durastante, F.</strong>; <strong>Serra-Capizzano, S.</strong>.
258         Optimizing a multigrid Runge-Kutta smoother for variable-coefficient
259         convection-diffusion equations. <em>Linear Algebra Appl.</em>  533  (2017),
260         507--535. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3695922"
261         target="_blank"><strong>MR3695922</strong></a>
262         <a href="/bibtex/Bertaccini2017b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
263       </li>
264       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
265         <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>.
266         Interpolating preconditioners for the solution of sequence of linear systems.
267         <EM>Comput. Math. Appl.</EM> <STRONG> 72 </STRONG> (2016),  no. 4, 1118--1130.
268         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3529065"
269         target="_blank"><strong>MR3529065</strong></a>
270         <a href="/bibtex/Bertaccini2016.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
271       </li>
272     </ul>
273   <td>
274 </tr>
275</table>
276
277Fractional calculus is that subset of Analysis that studies the possibilities of
278defining differential operators of real or complex order. After the definition
279of such objects, the need to numerically approximate the solution of differential
280equations defined in terms of them immediately arises. The following papers deal
281with the efficient numerical solution of different formulations of such problems.
282
283<table style="width:100%">
284  <colgroup>
285   <col span="1" style="width: 70%;">
286   <col span="1" style="width: 30%;">
287 </colgroup>
288 <tr>
289   <td>
290     <ul class="fa-ul">
291      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
292        <strong>Durastante, F.</strong>; <strong>Giscard, P.-L.</strong>;
293        <strong>Pozza, S.</strong>.
294        A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations.
295        <em>Fractional Calculus and Applied Analysis</em> (2026). 
296        <a href="/bibtex/Durastante2026b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
297        <a href="/papers/s13540-026-00529-2.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
298        <a href="https://link.springer.com/article/10.1007/s13540-026-00529-2" target="_blank">Open access</a>.
299      </li>
300      <li><span class="fa-li"><i class="fa-solid fa-book"></i></span>
301        Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers.
302        Springer INdAM Series (SINDAMS, volume 50). Editors: <strong>A. Cardone</strong>, <strong>M. Donatelli</strong>,
303        <strong>F. Durastante</strong>, <strong>R. Garrappa</strong>, <strong>M. Mazza</strong>,
304        <strong>M. Popolizio</strong>. (2023). Pages XII, 146. ISBN: 978-981-19-7715-2. ISSN: 2281-518X.
305      </li>
306      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
307        <strong>Aceto, L.</strong>; <strong>Durastante, F.</strong>. Efficient
308        computation of the Wright function and its applications to fractional
309        diffusion-wave equations. <em>ESAIM Math. Model. Numer. Anal.</em>
310        <strong> 56 </strong> (2022),  no. 6, 2181--2196.
311        <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4516169"><strong>MR4516169</strong></a>
312        <a href="/bibtex/Aceto2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
313        <a href="/papers/m2an220030.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
314      </li>
315       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
316         <strong>Durastante, F.</strong>. Efficient solution of time-fractional
317         differential equations with a new adaptive multi-term discretization of
318         the generalized Caputo-Dzherbashyan derivative.
319         <em>Calcolo</em> <strong> 56 </strong> (2019),  no. 4, Paper No. 36, 24 pp.
320         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4015149" target="_blank">
321           <strong>MR4015149</strong></a>
322         <a href="/bibtex/Durastante2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
323       </li>
324       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
325         <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>.
326         Efficient preconditioner updates for semilinear space-time fractional
327         reaction-diffusion equations. <em> Structured matrices in numerical linear algebra, </em>
328         285--302, Springer INdAM Ser., 30, <em>Springer, Cham,</em>  2019.
329         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3931580"
330         target="_blank"><strong>MR3931580</strong></a>
331         <a href="/bibtex/Bertaccini2019c.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
332       </li>
333       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
334         <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>
335         Block structured preconditioners in tensor form for the all-at-once
336         solution of a finite volume fractional diffusion equation.
337         <em>Appl. Math. Lett.</em>  95  (2019), 92--97.
338         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3936774"
339         target="_blank"><strong>MR3936774</strong></a>
340         <a href="/bibtex/Bertaccini2019b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
341       </li>
342       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
343         <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>.
344         Limited memory block preconditioners for fast solution of fractional partial
345         differential equations. <em>J. Sci. Comput.</em> <strong> 77 </strong>
346         (2018),  no. 2, 950--970.
347         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3860196" target="_blank">
348           <strong>MR3860196</strong></a>
349         <a href="/bibtex/Bertaccini2018.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
350       </li>
351       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
352         <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>.
353         Solving mixed classical and fractional partial differential equations
354         using short-memory principle and approximate inverses.
355         <em>Numer. Algorithms</em> <strong> 74 </strong> (2017),  no. 4, 1061--1082.
356         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3626328" target="
357         _blank">
358         <strong>MR3626328</strong></a>
359         <a href="/bibtex/Bertaccini2017.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
360       </li>
361     </ul>
362   </td>
363   <td style="text-align: center">Numerical treatment of Fractional Differential Equations</td>
364 </tr>
365 </table>
366
367Numerical optimal control theory is a part of numerical optimization that deals
368with the problem of finding a <em>control</em> for either a boundary value problem
369or a dynamical system over a period of time in such a way that an objective function
370is minimized/maximized. The prototypical problem of this type has the form
371$$ (y^*,u^*) = \arg\min_{u \in \mathcal{U}} J(y,u) = \frac{1}{2}\|y - y_z\|_2^2 + \frac{\lambda}{2} \| u \|_2^2, \text{ s.t. } e(y,u) = 0,$$
372where $\mathcal{U}$ is a function space containing the admissible controls, $y_z$
373a target state, and $e(y,u)=0$ a boundary value problem that the quantities $y$
374and $u$ have to satisfy. The numerical solution of such a problem is challenging
375in many ways, it mixes together optimization, differential, and linear algebra
376problems in a non-trivial way.
377 <table style="width:100%">
378   <colgroup>
379    <col span="1" style="width: 30%;">
380    <col span="1" style="width: 70%;">
381  </colgroup>
382  <tr>
383    <td style="text-align: center">
383Numerical optimal control of Partial Differential Equations</td>
384    <td>
385    <ul class="fa-ul">
386    <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
387      <strong>Durastante, F.</strong>; <strong>Furci, I.</strong>.
388      Spectral analysis of saddle-point matrices from optimization problems
389      with elliptic PDE constraints. <em>Electron. J. Linear Algebra</em>  36
390      (2020), 773--798.
391      <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4188673">
392        <strong>MR4188673</strong></a>
393    <a href="https://journals.uwyo.edu/index.php/ela/article/view/5151/5191">Open Access</a>.
394    <a href="/bibtex/Durastante2020.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
395    <a href="/papers/dopico,+vol36_pp773-798.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
396    </li>
397    <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
398    <strong>Durastante, F.</strong>; <strong>Cipolla, S.</strong>.
399    Fractional PDE constrained optimization: box and sparse constrained problems.
400    <em> Numerical methods for optimal control problems, </em>
401    111--135, Springer INdAM Ser., 29, <em>Springer, Cham,</em>  2018.
402    <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3889795"
403    target="_blank">
404    <strong>MR3889795</strong></a>
405    <a href="/bibtex/Cipolla2018b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
406    </li>
407    <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
408      <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>.
409      Fractional PDE constrained optimization: an optimize-then-discretize
410      approach with L-BFGS and approximate inverse preconditioning.
411      <em>Appl. Numer. Math.</em>  123  (2018), 43--57.
412      <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3711990"
413      target="_blank"><strong>MR3711990</strong></a>
414      <a href="/bibtex/Cipolla2018.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
415    </li>
416    </ul>
417    </td>
418  </tr>
419  </table>
420  A matrix function is simply a function which maps a matrix to another matrix,
421  indeed to maintain interesting properties one has to extend the concept of
422  scalar function to a matrix in a clever way. If, e.g., $f$ is a function
423  admitting a Taylor expansion with radius of convergence $r$, and $A$ is a
424  matrix such $\|A\| < r$ for any compatible norm $\|\cdot\|$, then $f(A)$ can
425  be defined as
426  $$ f(A) = \sum_{j=0}^{+\infty} c_k A^k, $$
427  for $c_k$ the Taylor coefficients of $f$. Equivalently, if $A$ is diagonalizable,
428  and $f$ is defined on the eigenvalues of $A$, then
429  $$ f(A) = X f(\Lambda) X^{-1}, \qquad A = X \Lambda X^{-1}, \; f(\Lambda)_{i,i} = f(\lambda_i(A)), $$
430  and in several other ways for more general $A$ and $f$. In any case, one of the
431  principal numerical task that one can face is the computation of Matrix-Function-vector
432  products, i.e., $\mathbf{y} = f(A)\mathbf{x}$, for $A$ a <em>large and sparse</em>
433  matrix. The following line of research deals with these kind of problems by
434  different techniques, and for different purposes (solution of Fractional
435  differential equations, network analysis, <em>etc.</em>).
436  <table style="width:100%">
437    <colgroup>
438     <col span="1" style="width: 70%;">
439     <col span="1" style="width: 30%;">
440   </colgroup>
441   <tr>
442     <td>
443       <ul class="fa-ul">
444         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
445         <strong>Aceto, L.</strong>; <strong>Durastante, F.</strong>.
446         Efficient computation of the sinc matrix function for the integration
447         of second-order differential equations. <em>Advances in Computational Mathematics</em> 
448         <strong>50</strong> (6), 109 (2024).
449         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4815175" target="_blank">
450         <strong>MR4815175</strong></a> 
451         <a href="/bibtex/Aceto2024b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
452         <a href="https://github.com/Cirdans-Home/rationalsecondorder" target="_blank"><i class="fa-solid fa-code"></i></a>
453         </li>
454         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
455         <strong>Aceto, L.</strong>; <strong>Durastante, F.</strong>.
456         Theoretical error estimates for computing the matrix logarithm by
457         Padé-type approximants. <em>Linear Multilinear Algebra</em> (2025), no 9., 2251-2270.
458         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4934074" target="_blank">
459         <strong>MR4934074</strong></a>
460         <a href="/bibtex/Aceto2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
461         <a href="https://github.com/Cirdans-Home/padelogarithm" target="_blank"><i class="fa-solid fa-code"></i></a>
462         </li>
463         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
464           <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>.
465           Computing function of large matrices by a preconditioned rational Krylov
466           method.
467           <em> Numerical mathematics and advanced applications ENUMATH 2019, </em>
468            343--351, Lect. Notes Comput. Sci. Eng., 139, <em>Springer, Cham,</em>
469            [2021], 2021. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4266513">
470            <strong>MR4266513</strong></a>
471            <a href="/bibtex/Bertaccini2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
472        </li>
473         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
474           <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>
475           Computing functions of very large matrices with small TT/QTT ranks
476           by quadrature formulas. <em>
476J. Comput. Appl. Math.</em>  370  (2020),
477           112663, 15 pp.
478           <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4046619"
479           target="_blank">
480           <strong>MR4046619</strong></a>
481           <a href="/bibtex/Bertaccini2020.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
482         </li>
483         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
484           <strong>Aceto, L.</strong>; <strong>Bertaccini, D.</strong>;
485           <strong>Durastante, F.</strong>; <strong>Novati, P.</strong>
486           Rational Krylov methods for functions of matrices with applications
487           to fractional partial differential equations.
488           <em>J. Comput. Phys.</em>  396  (2019), 470--482.
489           <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3989621"
490           target="_blank"><strong>MR3989621</strong></a>
491           <a href="/bibtex/Aceto2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
492         </li>
493         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
494           <strong>Bertaccini, D.</strong>; <strong>Popolizio, M.</strong>;
495           <strong>Durastante, F.</strong> Efficient approximation of functions
496           of some large matrices by partial fraction expansions.
497           <em>Int. J. Comput. Math.</em> <strong> 96 </strong> (2019),  no. 9,
498           1799--1817.
499           <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3960343"
500           target="_blank"><strong>MR3960343</strong></a>
501           <a href="/bibtex/Bertaccini2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
502         </li>
503       </ul>
504     </td>
505     <td style="text-align:center;"> Matrix-Functions </td>
506  </tr>
507  </table>
508  Network science is the study of complex networks that are nothing more than
509  graphs that are both not random and not structured, e.g., one usually does not
510  consider Cayley graphs encoding the structure of an abstract group.
511  Examples are telecommunication networks, computer networks, biological
512  networks, social networks, and many others. In each case, every actor is
513  represented by a vertex of the graph and their connections as an edge.
514  My interest in this field lies both in the modeling and the computational
515  aspects, specifically in the task of extracting information on the networked
516  phenomena by looking at the topology of the graph.
517  <table style="width:100%">
518    <colgroup>
519     <col span="1" style="width: 30%;">
520     <col span="1" style="width: 70%;">
521   </colgroup>
522   <tr>
523     <td style="text-align:center">Graphs and Network Science: Complex-Networks</td>
524     <td>
525     <ul class="fa-ul">
526      <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span>
527      <strong>Durastante, F.</strong>; <strong>Meini, B.</strong>; <strong>Saluzzi, L.</strong>
528      Steering dynamic network centrality via control theory.
529      <em>Submitted</em> (2026).
530      <a href="https://github.com/Cirdans-Home/optimal-network-control" target="_blank"><i class="fa-solid fa-code"></i></a>
531    <p style="text-align: right;"><a href="http://arxiv.org/abs/2607.14610" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p>
532  
533    </li>
534       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
535      <strong>Arrigo, F.</strong>; <strong>Durastante, F.</strong>
536      Walk based Laplacians for Modeling Diffusion on Complex Networks.
537      <em>J Sci Comput</em> 109, <strong>24</strong> (2026).
538      <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR5119477" target="_blank"><strong>MR5119477</strong></a>
539      <a href="/bibtex/Arrigo2026.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
540      <a href="https://github.com/Cirdans-Home/walk-laplacian" target="_blank"><i class="fa-solid fa-code"></i></a>
541      <a href="/papers/JOMP2026.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
542      <a href="https://link.springer.com/article/10.1007/s10915-026-03427-0" target="_blank">Open Access</a>
543      </li>
544       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
545       <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>;
546       <strong>Meini, B.</strong>
547       Enforcing Katz and PageRank Centrality Measures in Complex Networks. 
548       <em>SIAM J. Math. Data Sci.</em> <strong>
5487</strong> (2025), no. 3, 1514-1539.
549       <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4959962" target="_blank"><strong>MR4959962</strong></a>
550       <a href="/bibtex/Cipolla2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
551       <a href="https://github.com/Cirdans-Home/enforce-katz-and-pagerank" target="_blank"><i class="fa-solid fa-code"></i></a>
552       </li>
553       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
554        <strong>Benzi, M.</strong>; <strong>Durastante, F.</strong>;
555        <strong>Zigliotto, F.</strong>
556        Modelling advection on distance-weighted directed networks. 
557        <em>Math. Models Methods Appl. Sci.</em> <strong>35</strong> (2025), no. 5, 
558        1237-1265. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4896519" target="_blank"><strong>MR4896519</strong></a>
559        <a href="/bibtex/Benzi2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
560        <a href="https://github.com/francesco-zigliotto/graph-advection" target="_blank"><i class="fa-solid fa-code"></i></a>
561       </li>
562       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
563         <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>
564         Nonlocal diffusion of variable order on complex networks.
565         <em>Int. J. Comput. Math. Comput. Syst. Theory</em> <strong> 7 </strong>
566         (2022),  no. 3, 172--191.
567         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4483942" target="_blank"><strong>MR4483942</strong></a>
568         <a href="/bibtex/Bianchi2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
569       </li>
570       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
571         <strong>Bianchi, D.</strong>; <strong>Donatelli, M.</strong>;
572         <strong>Durastante, F.</strong>; <strong>Mazza, M.</strong>.
573         Compatibility, embedding and regularization of non-local random
574         walks on graphs. <em>J. Math. Anal. Appl.</em> <strong> 511</strong>
575         (2022),  no. 1, Paper No. 126020, 30 pp.
576         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4379318" target="_blank">
577           <strong>MR4379318</strong></a>
578         <a href="/bibtex/Bianchi2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
579       </li>
580       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
581         <strong>Arrigo, F.</strong>; <strong>Durastante, F.</strong>.
582         Mittag–Leffler Functions and their Applications in Network Science.
583         <em>SIAM J. Matrix Anal. Appl.</em> <strong> 42 </strong> (2021),
584         no. 4, 1581--1601. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4340667"
585         target="_blank"><strong>MR4340667</strong></a>
586         <a href="/bibtex/Arrigo2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
587       </li>
588       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
589         <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>;
590         <strong>Tudisco, F.</strong>. Nonlocal pagerank.
591         <em>ESAIM Math. Model. Numer. Anal.</em> <strong> 55 </strong> (2021),
592         no. 1, 77--97.
593         <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4216832"
594         target="_blank"><strong>MR4216832</strong></a>
595         <a href="/bibtex/Cipolla2021b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
596         <a href="/papers/m2an200017.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
597       </li>
598       <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
599         <strong>Benzi, M.</strong>; <strong>Bertaccini, D.</strong>;
600         <strong>Durastante, F.</strong>; <strong>Simunec, I.</strong>.
601         Non-local network dynamics via fractional graph Laplacians.
602         <em>J. Complex Netw.</em> <strong> 8 </strong> (2020),  no. 3, cnaa017,
603         29 pp. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4130854"
604         target="_blank"><strong>MR4130854</strong></a>
605         <a href="/bibtex/Benzi2020.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
606      </li>
607     </ul>
608     </td>
609  </tr>
610  </table>
611<p>
612  Numerical algorithms for Markov chains are essential tools in the analysis of stochastic processes.
613  A Markov chain is defined by a transition matrix $ P $, where $ P_{ij} $ represents the probability
614  of moving from state $ i $ to state $ j $. A central computational task is finding the stationary
615  distribution $ \pi $, satisfying $ \pi P = \pi $ and $ \sum_i \pi_i = 1 $. Beyond stationarity,
616  algorithms also address the <em>embeddability problem</em>, which seeks a generator matrix $ Q $
617  such that $ P = e^{Q} $, characterizing $ P $ as the discretization of a continuous-time Markov process.
618  Another important property is <em>reversibility</em>, where $ \pi_i P_{ij} = \pi_j P_{ji} $ for all $ i, j $,
619  which simplifies analysis and enables structure-preserving approximations. Additionally, computing
620  the <em>Kemeny constant</em>, defined as $ K = \sum_{j} m_{ij} \pi_j $ (independent of $ i $), where
621  $ m_{ij} $ is the expected number of steps to reach state $ j $ from $ i $, provides insight into
622  the overall mixing behavior of the chain. Efficient numerical methods, including Riemannian optimization,
623  sparse and dense linear solvers, eigendecomposition techniques, are key to tackling these challenges
624  at scale.
625</p>
626  <table style="width:100%">
627    <colgroup>
628     <col span="1" style="width: 30%;">
629     <col span="1" style="width: 70%;">
630   </colgroup>
631  <tr>
632  <td style="text-align: center">
633    Numerical methods for Markov Chains
634  </td>
635  <td>
636    <ul class="fa-ul">
637      <li><span class="fa-li"><i class="fa-regular fa-square"></i></span>
638      <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>; <strong>Gnazzo, M.</strong>, <strong>Meini, B.</strong>.
639      Nearest Reversible Markov Chains with Sparsity Constraints: An Optimization Approach.
640      Low-Rank Structures and Numerical Methods in Matrix and Tensor Computations.
641      <em>Springer INdAM Series (SINDAMS, volume XX)</em>. <strong>Accepted</strong> (2026). 
642      <a href="https://github.com/Cirdans-Home/sparse-reversible" target="_blank"><i class="fa-solid fa-code"></i></a>
643      <p style="text-align: right;"><a href="https://arxiv.org/abs/2602.23059" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p>
644
645      </li> 
646      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
647      <strong>Durastante, F.</strong>; <strong>Gnazzo, M.</strong>; <strong>Meini, B.</strong>.
648      Kemeny’s constant minimization for reversible Markov chains via structure-preserving perturbations.
649      <em>Bit Numer Math</em> <strong>66</strong> (2026), no. 59. 
650      <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=5134555" target="_blank"><strong>MR5134555</strong></a> 
651      <a href="https://doi.org/10.1007/s10543-026-01152-6" target="_blank"><i class="fa-solid fa-unlock-keyhole"></i>Open Access </a>
652      <a href="/bibtex/Durastante2026d.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
653      <a href="https://github.com/Cirdans-Home/optimize-kemeny" target="_blank"><i class="fa-solid fa-code"></i></a>
654      <a href="/papers/s10543-026-01152-6.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
655      </li>
656      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
657      <strong>Durastante, F.</strong>; <strong>Gnazzo, M.</strong>, <strong>Meini, B.</strong>.
658      A Riemannian Optimization Approach for Finding the Nearest Reversible Markov Chain.
659      <em>Numer. Linear Algebra Appl.</em> <strong>33</strong> (2026), no. 4, Paper no. e70112. 
660      <a href="https://mathscinet.ams.org/mathscinet/article?mr=5115561" target="_blank"><strong>MR5115561</strong></a>
661      <a href="/bibtex/Durastante2026c.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
662      <a href="https://github.com/miryamgnazzo/nearest-reversible" target="_blank"><i class="fa-solid fa-code"></i></a>
663      </li>  
664      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
665      <strong>Durastante, F.</strong>; <strong>Meini, B.</strong>.
666      Stochastic $p$th root approximation of a stochastic matrix: A Riemannian
667      optimization approach. <em>SIAM J. Matrix Anal. Appl.</em>  <strong> 45 </strong> (2024),
668      no. 2, 875--904. <a href="https://mathscinet.ams.org/mathscinet/article?mr=4734557" target="_blank"><strong>MR4734557</strong></a>
669      <a href="/bibtex/Meini2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
670      <a href="https://fdurastante.github.io/courses/markovslides/markovrootsslides.html#/" target="_blank"><i class="fa-solid fa-person-chalkboard"></i></a>
671      <a href="https://gist.github.com/Cirdans-Home/76ab38cbd922e56caebc526087569ad5" target="_blank"><i class="fa-brands fa-github-alt"></i></a>
672      <a href="https://github.com/Cirdans-Home/pth-root-stochastic" target="_blank"><i class="fa-solid fa-code"></i></a>
673      </li>
674      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
675      <strong>Bini, D. A.</strong>; <strong>Durastante, F.</strong>;
676      <strong>Kim, S.</strong>; <strong>Meini, B.</strong>
677      On Kemeny's constant and stochastic complement. <em>Linear Algebra Appl.</em> 
678    <strong>
678703</strong> (2024), 137-162. <a href="https://mathscinet.ams.org/mathscinet/article?mr=4797227" target="_blank"><strong>MR4797227</strong></a>
679    <a href="/papers/LAA2024.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> <a href="https://doi.org/10.1016/j.laa.2024.09.001" target="_blank">Open access</a> <a href="/bibtex/Bini2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> <a href="https://github.com/Cirdans-Home/Kemeny-and-Conquer" target="_blank"><i class="fa-brands fa-github"></i></a>
680      </li>
681   </ul>
682  </td>
683  </tr>
684  </table>
685<p>Inverse problems are involved in the task of inferring the parameters of the
686model from a set of (possibly noisy) measurements requires. These types of
687problems can be difficult to solve for several reasons, e.g., one could be
688dealing with a lack of unicity, that is: different values of parameters are
689consistent with the measurement, and discovering the parameters may be
690challenging from the computational point of view. I have done some work in using
691linear algebra techniques for a particular type of inverse problem that is
692<em>image denoise and deblurring</em>, that is the process of removing blurring
693artifacts and noise from images (e.g., somebody shook the camera while we were
694taking the photo).</p>
695  <table style="width:100%">
696    <colgroup>
697     <col span="1" style="width: 70%;">
698     <col span="1" style="width: 30%;">
699   </colgroup>
700  <tr>
701  <td>
702    <ul class="fa-ul">
703      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
704        <strong>Cipolla, S.</strong>; <strong>Donatelli, M.</strong>;
705        <strong>Durastante, F.</strong>. Regularization of Inverse
706        Problems by an Approximate Matrix–Function Technique.
707        <em>Numer. Algorithms</em> <strong>88</strong> (2021), 1275-1308.
708        DOI. <a href="https://link.springer.com/article/10.1007/s11075-021-01076-y" target="_blank">10.1007/s11075-021-01076-y</a>.
709        <a href="/bibtex/Cipolla2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
710        <a href="/papers/s11075-021-01076-y.pdf" target="_blank"><i class="fa-regular "></i></a>
711     </li>
712      <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
713        <strong>Cipolla, S.</strong>; <strong>Di Fiore, C.</strong>;
714        <strong>Durastante, F.</strong>; <strong>Zellini, P.</strong>.
715        Regularizing properties of a class of matrices including the optimal and
716        the superoptimal preconditioners. <em>Numer. Linear Algebra Appl.</em>
717        <strong> 26 </strong> (2019),  no. 2, e2225, 17 pp.
718        <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3911025"
719        target="_blank"><strong>MR3911025</strong></a> <a href="/bibtex/Cipolla2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
720     </li>
721   </ul>
722  </td>
723  <td style="text-align: center">
724    Regularization and Inverse Problems
725  </td>
726  </tr>
727  </table>
728  <p>Optimization tasks involve the process of finding the best possible solution from a vast, often 
729    overwhelmingly large, set of valid options. These types of problems can be exceptionally difficult for 
730    classical computers to solve because the number of potential combinations grows exponentially, making an 
731    exhaustive search practically impossible. Quantum computing introduces a fundamentally different approach 
732    by leveraging quantum mechanical properties—such as superposition and entanglement—to evaluate complex solution 
733    spaces much more efficiently. I have done some work in exploring how quantum algorithms can be applied 
734    to tackle these computationally demanding tasks, focusing on how we can harness quantum phenomena to 
735    accelerate the discovery of optimal states (e.g., calculating the most efficient delivery routes 
736    for a massive logistics network or optimizing complex financial portfolios).
737  </p>
738   <table style="width:100%">
739    <colgroup>
740     <col span="1" style="width: 30%;">
741     <col span="1" style="width: 70%;">
742   </colgroup>
743  <tr>
744  <td style="text-align: center">
745    Quantum Computing and Optimization
746  </td>
747  <td>
748    <ul class="fa-ul">
749      <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span>
750        <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>.
751        Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA
752        <em>Submitted</em> (2026).
753        <p style="text-align: right;"><a href="https://arxiv.org/abs/2606.28536" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p>
754
755      </li>
756    </ul>
757  </td>
758  </tr>
759  </table>  
760  <p>Mathematical methods play also a role in unexpected settings like archaeology.
761  They enable the analysis and interpretation of data, making predictions, and
762  gaining insights into quantitatives aspects. Statistical techniques are commonly
763  employed to analyze large datasets, such as excavation records, artifact distributions,
764  and survey data. These methods help archaeologists identify patterns, trends,
765  and correlations, allowing them to make inferences about past human behaviors
766  and societal structures. Mathematical modeling is also utilized to reconstruct
767  ancient landscapes, simulate settlement patterns, and explore the dynamics
768  of cultural change over time. The integration of mathematics into archaeological
769  investigations enhances the accuracy, precision, and efficiency of research,
770  contributing to a quantitative understanding of some aspects of history.</p>
771  <table style="width: 100%">
772    <colgroup>
773     <col span="1" style="width: 70%;">
774     <col span="1" style="width: 30%;">
775   </colgroup>
776   <tr>
777     <td>
778       <ul class="fa-ul">
779         <li><li><span class="fa-li"><i class="fas fa-check-square"></i></span>
780           <strong>Mauro, C.</strong>;   <strong>Durastante, F.</strong>; <strong>Díaz-Sánchez, C.</strong>.
781           A Light in the Dark: The Role of Coastal Lights in Night Navigation in Antiquity
782           <em>Journal of Eastern Mediterranean Archaeology and Heritage Studies</em> <strong>13</strong> (2025), no. 4, 367-380.
783           <a href="/bibtex/Mauro2025b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 
784           <a href="https://doi.org/10.5325/jeasmedarcherstu.13.4.0367" target="_blank"><i class="fa-solid fa-link"></i></a>
785        </li>
786        <li><li><span class="fa-li"><i class="fas fa-check-square"></i></span>
787          <strong>Mauro, C.</strong>;   <strong>Durastante, F.</strong>. 
788          On the use of lights in nocturnal seafaring during Antiquity 
789          <em>International Journal of Nautical Archaeology</em> (2025), 1-8 pp. 
790          <a href="/bibtex/Mauro2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 
791          <a href="https://doi.org/10.1080/10572414.2025.2525130" target="_blank"><i class="fa-solid fa-link"></i></a>
792        </li>
793         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
794         <strong>Mauro, C.</strong>;  <strong>Durastante, F.</strong>.
795         Nocturnal Seafaring: the Reduction of Visibility at Night and its Impact on Ancient Mediterranean Seafaring.
796         A Study Based on 8-4th Centuries BC Evidence <em>Journal of Maritime Archaeology</em>, (2024), 1-19 pp.
797         <a href="/bibtex/Mauro2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
798         <a href="/papers/JNA2024.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a>
799         <a href="https://doi.org/10.1007/s11457-023-09385-0" target="_blank">Open access</a>
800         </li>
801         <li><span class="fa-li"><i class="fas fa-check-square"></i></span>
802           <strong>Mauro, C.</strong>;   <strong>Durastante, F.</strong>.
803           Evaluating visibility at sea: Instrumental data and historical nautical
804           records. Mount Etna from the Calabrian Ionian coast (Italy).
805           <em>The Journal of Island and Coastal Archaeology, 17.1</em> (2022),
806           21-42 pp. <a href="/bibtex/Mauro2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
807        </li>
808      </ul>
809     </td>
810     <td style="text-align: center">Applications, intersections, contaminations</td>
811   </tr>
812  </table>
813
814  <!--
815 <h3> Projects </h3>
816
817<ul class="fa-ul">
818  <li><span class="fa-li"><i class="fas fa-people-carry"></i></span>
819  Member of the Horizon Europe project "dealii-X: an Exascale Framework for Digital Twins of the Human Body",
820  funded by the European Union's Horizon 2020 research and innovation programme under <a href="https://cordis.europa.eu/project/id/101172493" target="_blank">grant agreement No 101172493</a>, 
821  and financed with € 3 939 780,00.
822  </li>
823  <li><span class="fa-li"><i class="fas fa-coins"></i></span>
824    Fundings for € 4000.00 for the "Progetti Speciali per la Didattica
825    Università di Pisa 2023/24". Project: <em>High-Performance Mathematics</em>.
826  </li>
827  <li><span class="fa-li"><i class="fas fa-coins"></i></span>
828  Funding for 4950.00 € for the 2024 GNCS INdAM project "Metodi di riduzione di
829  modello ed approssimazioni di rango basso per problemi alto-dimensionali".
830  P.I. C. Pagliantini. Participants:  L. Aceto, F. Durastante, B, Meini, F.G.
831  Poloni, L, Robol, M, Strazzullo, A. Bucci, A. A. Casulli, L. Saluzzi, I. Simunec.
832  </li>
833  <li><span class="fa-li"><i class="fas fa-people-carry"></i></span>
834    Collaborator as research associate to the Istituto per le Applicazioni del
835    Calcolo "Mauro Picone" of the National Research Council of Italy to the
836    2024-2026 Energy Oriented Center of Excellence (EoCoE III): Fostering the European
837    Energy Transition with Exascale A Center of Excellence in Computing Applications.
838    EuroHPC Project, Horizon Europe Program for Research and Innovation.  </li>
839  <li><span class="fa-li"><i class="fa-solid fa-server"></i></span>
840    EuroHPC Project DD-23-167, Sparse Matrix Computations at Extreme Scales for
841    the access to the Karolina supercomputer at the e-INFRA CZ facilities (Czech Republic),
842    from 5/12/2023.
843  </li>
844  <li><span class="fa-li"><i class="fas fa-coins"></i></span> Funding for 5600.00 €
845  for the 2023 GNCS INdAM project "Metodi basati su matrici e tensori strutturati
846  per problemi di algebra lineare di grandi dimensioni". P.I.  S. Massei.
847  Participants: F. Durastante, L. Robol, B. Meini, F. Poloni,
848M. Benzi, B. Iannazzo, L. Aceto, I. Simunec, C. Faccio, M. Rinelli, A.
849Bucci, M. Viviani. </li>
850  <li><span class="fa-li"><i class="fa-solid fa-chalkboard-user"></i></span> Fundings for
851    € 5943,65 for the "Progetti Speciali per la Didattica
852  Università di Pisa 2022/23". Project: <em>Calcolo Parallelo dall'Infrastruttura alla Matematica</em>.</li>
853  <li><span class="fa-li"><i class="fa-solid fa-server"></i></span>
854  Leonardo Early Access Program (LEAP). Awarderd computing time on the
855  Leonardo HPC System for the project
856  "PSCToolkit for Sparse Matrix Computations at Extreme Scales". Principal
857  Investigator S. Filippone and Co-Principal Investigator P. D'Ambra.
858  Participants: S. Filippone, P. D'Ambra, F. Durastante, V. Cardellini, A. Celestini.
859  </li>
860  <li><span class="fa-li"><i class="fas fa-coins"></i></span>Funding for 2700.00 €
861  for the 2022 GNCS INdAM project "Metodi numerici per l’analisi di modelli
862  innovativi di reti complesse" with Principal Investigator: Fabio Durastante
863  and participants: B. Meini, P. Boito, S. Massei, G. Del Corso, M. Benzi,
864  D. Bertaccini, P. D'Ambra, B. Iannazzo, A. Bucci, C. Faccio, M. Rinelli,
865  I. Simunec.</li>
866  <li><span class="fa-li"><i class="fas fa-coins"></i></span>Funding for 11656.03 €
867  for the project "¿Ver o no ver? Una aproximación interdisciplinar a los
868  estudios de visibilidad en el contexto de la navegación antigua (siglos IX-IV a.C.)."
869  (PR27/21-018) co-financed by the Comunidad de Madrid and the Universidad
870  Complutense. Principal Investigator C. M. Mauro. </li>
871  <li><span class="fa-li"><i class="fas fa-people-carry"></i></span> Member of
872    the Work-Package 6 (WP6) "Applications and Use cases" in the European
873    <a href="https://textarossa.eu/" target="_blank">TEXTAROSSA</a> project.
874  </li>
875  <li><span class="fa-li"><i class="fas fa-coins"></i></span> Funding for
876  15000€ for the organization of the INdAM workshop on "Fractional Differential Equations:
877  Modeling, Discretization, and Numerical Solvers" (<a
878  href="https://fractionalworkshop.github.io/" target="_blank">
879  https://fractionalworkshop.github.io/</a>). Organizing committee:
880    Angelamaria Cardone, Marco Donatelli, Fabio Durastante, Roberto Garrappa,
881    Mariarosa Mazza, Marina Popolizio.
882   </li>
883   <li><span class="fa-li"><i class="fas fa-people-carry"></i></span> Member of
884     the Work-Package 3 (WP3) "Scalable Solvers" in the European
885     <a href="https://www.eocoe.eu" target="_blank">EoCoE-II</a> project.
886     <ul>
887       <li>Writer for the Deliverable: ``D3.2
888		Preliminary results and performance evaluation of
889		Linear Algebra solvers'',</li>
890      <li>Contributor for the Deliverable: ``D3.3
891		Updated results and new releases of LA solvers.''</li>
892     </ul>
893   </li>
894   <li><span class="fa-li"><i class="fas fa-coins"></i></span>
895     Funding for 1200€ for the 2020 GNCS-INDAM Project "Nonlocal models for
896     the analysis of complex networks" with Principal Investigator F. Durastante </li>
897   <li><span class="fa-li"><i class="fas fa-coins"></i></span>
898     Funding for 3400€ for the 2019 GNCS-INDAM Project "Tecniche innovative e
899parallele per sistemi lineari e non lineari di grandi dimensioni, funzioni ed equazioni
900matriciali ed applicazioni" with Principal Investigator D. Bertaccini together
901with L. Bergamaschi, P. D’Ambra, M. Ferronato, C. Janna, F. Marcuzzi, A.
902Martinez Calomardo, V. Simoncini, M. Porcelli, D. Brandoni
903   </li>
904   <li><span class="fa-li"><i class="fas fa-coins"></i></span>
905     Funding for 4500€ for the 2018 GNCS-INDAM project "Tecniche innovative
906per problemi di algebra lineare" with Principal Investigator D. Bertaccini together
907with D. Bini, G. Del Corso, D. Fasino, L. Gemignani, B. Iannazzo, N.
908Mastronardi, B. Meini, F. Poloni, A. Fayyaz, P. Boito, M. Fasi, I. Furci, S.
909Massei and L. Robol.
910   </li>
911 </ul>
912-->
913 <h3> Membership in scientific societies </h3>
914
915 <ul class="fa-ul">
916   <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span>
917     Istituto Nazionale di Alta Matematica (INdAM) - Gruppo Nazionale di Calcolo Scientifico (GNCS).
918   </li>
919   <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span>
920     Società Italiana di Matematica Applicata e Industriale (SIMAI).
921   </li>
922   <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span>
923     Society of Industrial and Applied Mathematics (SIAM) - Activity group in Linear Algebra.
924   </li>
925   <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span>
926     International Linear Algebra Society (ILAS).
927   </li>
928   <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span>
929     Unione Matematica Italiana (UMI).
930   </li>
931   <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span>
932     ACM: Association for Computing Machinery.
933   </li>
934 </ul>
935
936 <h3> Collaboration Network </h3>
937
938 Most of the work described here has been done with several collaborators. I am
939 always working on expanding my network of collaborators by looking for people to
940 do interesting things with.
941
942 <iframe src="/network.html" width="100%" height="450px" style="border:none;"
943    title="Collaboration Network"></iframe>
944
945 <h3> Bibliometric indexes  </h3>
946 <q>Not everything that counts can be counted, and not everything that can be counted counts.</q><br>
947  <table>
948  <tr>
949    <td><img src="/assets/img/FDhIndex.png" width="80%" alt="H-Index"></td>
950    <td><img src="/assets/img/FDSubjectAreas.png" width="80%" alt="Subject Areas"></td>
951  </tr>
952  <tr>
953    <td style="text-align: center;">(Scopus) H-Index: 10</td>
954    <td style="text-align: center;">(Scopus) Subject Areas</td>
955  </tr>
956  </table>
957
958<h2> Editorial Work </h2>
959
960I serve as editor for:
961<ul class="fa-ul">
962  <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> <a href="http://www.springer.com/mathematics/applications/journal/40314" target="_blank">Computational and Applied Mathematics</a> (Comput. Appl. Math.)</li>
963  <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> <a href="https://jmm.guilan.ac.ir/" target="_blank">Journal of Mathematical Modeling</a> (J. Math. Model.)</li>
964</ul>
965<br>
966I have been part of the
967<ul class="fa-ul">
968  <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> AD/AE The 7th Annual Parallel Applications Workshop,
969Alternatives To MPI+X Sunday, November 17, 2024 held in conjunction with SuperComputing 17-22 November 2024, Atlanta.</li>
970  <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> AD/AE Appendices Process & Badges committee for the I Am HPC International Conference for High Performance
971Computing, Networking, Storage, and Analysis; Denver, Colorado November 12-17, 2023.</li>
972  <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> Member of the Program Committee for the 9th International Conference on Scale Space and Variational Methods in Computer Vision May 21-25 2023, Sardinia - Italy</li>
973</ul>
974<br>
975
976I have served as reviewer for manuscripts submitted to the following journals.<br>
977<table>
978<tr>
979  <td><a href="https://www.scimagojr.com/journalsearch.php?q=25708&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25708" alt="SCImago Journal &amp; Country Rank"  /></a> </td>
980  <td><a href="https://www.scimagojr.com/journalsearch.php?q=26425&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=26425" alt="SCImago Journal &amp; Country Rank"  /></a></td>
981  <td><a href="https://www.scimagojr.com/journalsearch.php?q=26419&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=26419" alt="SCImago Journal &amp; Country Rank"  /></a></td>
982  <td><a href="https://www.scimagojr.com/journalsearch.php?q=61774&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=61774" alt="SCImago Journal &amp; Country Rank"  /></a></td>
983</tr>
984<tr>
985  <td><a href="https://www.scimagojr.com/journalsearch.php?q=25170&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25170" alt="SCImago Journal &amp; Country Rank"  /></a></td>
986  <td><a href="https://www.scimagojr.com/journalsearch.php?q=25307&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25307" alt="SCImago Journal &amp; Country Rank"  /></a></td>
987  <td><a href="https://www.scimagojr.com/journalsearch.php?q=25712&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25712" alt="SCImago Journal &amp; Country Rank"  /></a></td>
988  <td><a href="https://www.scimagojr.com/journalsearch.php?q=25713&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25713" alt="SCImago Journal &amp; Country Rank"  /></a></td>
989</tr>
990<tr>
991  <td><a href="https://www.scimagojr.com/journalsearch.php?q=27856&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=27856" alt="SCImago Journal &amp; Country Rank"  /></a></td>
992  <td><a href="https://www.scimagojr.com/journalsearch.php?q=18534&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=18534" alt="SCImago Journal &amp; Country Rank"  /></a></td>
993  <td><a href="https://www.scimagojr.com/journalsearch.php?q=18120&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=18120" alt="SCImago Journal &amp; Country Rank"  /></a></td>
994  <td><a href="https://www.scimagojr.com/journalsearch.php?q=28067&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=28067" alt="SCImago Journal &amp; Country Rank"  /></a> </td>
995</tr>
996<tr>
997  <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100422153&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100422153" alt="SCImago Journal &amp; Country Rank"  /></a></td>
998  <td><a href="https://www.scimagojr.com/journalsearch.php?q=26415&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=26415" alt="SCImago Journal &amp; Country Rank"  /></a></td>
999  <td><a href="https://www.scimagojr.com/journalsearch.php?q=23847&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=23847" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1000  <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100830702&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100830702" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1001</tr>
1002<tr>
1003  <td><a href="https://www.scimagojr.com/journalsearch.php?q=19900193816&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=19900193816" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1004  <td><a href="https://www.scimagojr.com/journalsearch.php?q=24557&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=24557" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1005  <td><a href="https://www.scimagojr.com/journalsearch.php?q=19900192450&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=19900192450" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1006  <td><a href="https://www.scimagojr.com/journalsearch.php?q=24557&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=24557" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1007</tr>
1008<tr>
1009  <td> <a href="https://www.scimagojr.com/journalsearch.php?q=21100201542&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100201542" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1010  <td><a href="https://www.scimagojr.com/journalsearch.php?q=28494&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=28494" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1011  <td><a href="https://www.scimagojr.com/journalsearch.php?q=5000153703&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=5000153703" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1012  <td><a href="https://www.scimagojr.com/journalsearch.php?q=4000149606&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=4000149606" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1013</tr>
1014<tr>
1015  <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100287116&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100287116" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1016  <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100927407&amp;tip=sid&amp;exact=no" title="SCImago Journal &amp; Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100927407" alt="SCImago Journal &amp; Country Rank"  /></a></td>
1017</tr>
1018</table>
1019
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