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1. Conditional upper and lower bounds for $L$-functions in the Selberg class close to the critical line

Author

Palojärvi, Neea and Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11M06, 11M26, 41A30
Abstract

Assuming the Generalized Riemann Hypothesis, we provide uniform upper and lower bounds with explicit main terms for $\log{\left|\mathcal{L}(s)\right|}$ for $\sigma \in (1/2,1)$ and for functions in the Selberg class. We also provide estimates under additional assumptions on the distribution of Dirichlet coefficients of $\mathcal{L}(s)$ on prime numbers. Moreover, by assuming a polynomial Euler product representation for $\mathcal{L}(s)$, we establish both uniform bounds, and completely explicit estimates by assuming also the strong $\lambda$-conjecture.

Published
2024

2. Conditional estimates for $L$-functions in the Selberg class

Author

Palojärvi, Neea and Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11M06, 11M26, 41A30
Abstract

Assuming the Generalized Riemann Hypothesis, we provide uniform upper bounds with explicit main terms for moduli of $\left(\cL'/\cL\right)(s)$ and $\log{\cL(s)}$ for $1/2+\delta\leq\sigma<1$, fixed $\delta\in(0,1/2)$ and for functions in the Selberg class except for the identity function. We also provide estimates under additional assumptions on the distribution of Dirichlet coefficients of $\cL(s)$ on prime numbers. Moreover, by assuming a polynomial Euler product representation for $\cL(s)$, we establish uniform bounds for $|3/4-\sigma|\leq 1/4-1/\log{\log{\left(\sq|t|^{\sdeg}\right)}}$, $|1-\sigma|\leq 1/\log{\log{\left(\sq|t|^{\sdeg}\right)}}$ and $\sigma=1$, and completely explicit estimates by assuming also the strong $\lambda$-conjecture.

Published
2022

3. Conditional estimates for the logarithmic derivative of Dirichlet $L$-functions

Author

Chirre, Andrés, Simonič, Aleksander, and Hagen, Markus Valås

Subjects
Mathematics - Number Theory, 11M06, 11M26, 41A30
Abstract

Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$-aspect for the logarithmic derivative $\left(L'/L\right)\left(\sigma,\chi\right)$ of Dirichlet $L$-functions, where $\chi$ is a primitive character modulo $q\geq 10^{30}$ and $1/2+1/\log{\log{q}}\leq\sigma\leq 1-1/\log\log q$. In addition, for $\sigma=1$ we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given., Comment: 11 pages

Published
2022
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4. Estimates for $L$-functions in the critical strip under GRH with effective applications

Author

Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11M06, 11M26, 11N37
Abstract

Assuming the Generalized Riemann Hypothesis, we provide explicit upper bounds for moduli of $\log{\mathcal{L}(s)}$ and $\mathcal{L}'(s)/\mathcal{L}(s)$ in the neighbourhood of the 1-line when $\mathcal{L}(s)$ are the Riemann, Dirichlet and Dedekind zeta-functions. To do this, we generalize Littlewood's well known conditional result to functions in the Selberg class with a polynomial Euler product, for which we also establish a suitable convexity estimate. As an application we provide conditional and effective estimate for the Mertens function., Comment: 20 pages

Published
2022

5. Explicit estimates for $\zeta(s)$ in the critical strip under the Riemann Hypothesis

Author

Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11M26, 11N37, 11Y35
Abstract

Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for $\left|\zeta(s)\right|$ right to the critical line. As an application we make explicit Titchmarsh's conditional bound for the Mertens function and Montgomery--Vaughan's conditional bound for the number of $k$-free numbers., Comment: 24 pages, additional remarks

Published
2021

7. Atkinson's formula for the mean square of $\zeta(s)$ with an explicit error term

Author

Simonič, Aleksander and Starichkova, Valeriia V.

Subjects
Mathematics - Number Theory, 11M06, 11N37, 11Y35
Abstract

We provide an explicit $O\left(\log^2{T}\right)$-term of the celebrated Atkinson's formula for the error term $E(T)$ of the second power moment of the Riemann zeta-function on the critical line. As an application, we obtain an explicit version of well-known estimate $E(T)\ll_{\varepsilon} T^{\frac{1}{3}+\varepsilon}$., Comment: 42 pages, 1 figure, 2 tables

Published
2021
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8. Adaptive Robotic Levering for Recycling Tasks

Author

Kuster, Boris, Simonič, Mihael, Ude, Aleš, Ceccarelli, Marco, Series Editor, Agrawal, Sunil K., Advisory Editor, Corves, Burkhard, Advisory Editor, Glazunov, Victor, Advisory Editor, Hernández, Alfonso, Advisory Editor, Huang, Tian, Advisory Editor, Jauregui Correa, Juan Carlos, Advisory Editor, Takeda, Yukio, Advisory Editor, Petrič, Tadej, editor, Ude, Aleš, editor, and Žlajpah, Leon, editor

Published
2023
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9. Biallelic CRELD1 variants cause a multisystem syndrome, including neurodevelopmental phenotypes, cardiac dysrhythmias, and frequent infections

Author

Borras, Silvia, Clark, Caroline, Dean, John, Miedzybrodzka, Zosia, Ross, Alison, Tennant, Stephen, Dabir, Tabib, Donnelly, Deirdre, Humphreys, Mervyn, Magee, Alex, McConnell, Vivienne, McKee, Shane, McNerlan, Susan, Morrison, Patrick J., Rea, Gillian, Stewart, Fiona, Cole, Trevor, Cooper, Nicola, Cooper-Charles, Lisa, Cox, Helen, Islam, Lily, Jarvis, Joanna, Keelagher, Rebecca, Lim, Derek, McMullan, Dominic, Morton, Jenny, Naik, Swati, O’Driscoll, Mary, Ong, Kai-Ren, Osio, Deborah, Ragge, Nicola, Turton, Sarah, Vogt, Julie, Williams, Denise, Bodek, Simon, Donaldson, Alan, Hills, Alison, Low, Karen, Newbury-Ecob, Ruth, Norman, Andrew M., Roberts, Eileen, Scurr, Ingrid, Smithson, Sarah, Tooley, Madeleine, Abbs, Steve, Armstrong, Ruth, Dunn, Carolyn, Holden, Simon, Park, Soo-Mi, Paterson, Joan, Raymond, Lucy, Reid, Evan, Sandford, Richard, Simonic, Ingrid, Tischkowitz, Marc, Woods, Geoff, Bradley, Lisa, Comerford, Joanne, Green, Andrew, Lynch, Sally, McQuaid, Shirley, Mullaney, Brendan, Berg, Jonathan, Goudie, David, Mavrak, Eleni, McLean, Joanne, McWilliam, Catherine, Reavey, Eleanor, Azam, Tara, Cleary, Elaine, Jackson, Andrew, Lam, Wayne, Lampe, Anne, Moore, David, Porteous, Mary, Baple, Emma, Baptista, Júlia, Brewer, Carole, Castle, Bruce, Kivuva, Emma, Owens, Martina, Rankin, Julia, Shaw-Smith, Charles, Turner, Claire, Turnpenny, Peter, Tysoe, Carolyn, Bradley, Therese, Davidson, Rosemarie, Gardiner, Carol, Joss, Shelagh, Kinning, Esther, Longman, Cheryl, McGowan, Ruth, Murday, Victoria, Pilz, Daniela, Tobias, Edward, Whiteford, Margo, Williams, Nicola, Barnicoat, Angela, Clement, Emma, Faravelli, Francesca, Hurst, Jane, Jenkins, Lucy, Jones, Wendy, Ajith Kumar, V.K., Lees, Melissa, Loughlin, Sam, Male, Alison, Morrogh, Deborah, Rosser, Elisabeth, Scott, Richard, Wilson, Louise, Beleza, Ana, Deshpande, Charu, Flinter, Frances, Holder, Muriel, Irving, Melita, Izatt, Louise, Josifova, Dragana, Mohammed, Shehla, Molenda, Aneta, Robert, Leema, Roworth, Wendy, Ruddy, Deborah, Ryten, Mina, Yau, Shu, Bennett, Christopher, Blyth, Moira, Campbell, Jennifer, Coates, Andrea, Dobbie, Angus, Hewitt, Sarah, Hobson, Emma, Jackson, Eilidh, Jewell, Rosalyn, Kraus, Alison, Prescott, Katrina, Sheridan, Eamonn, Thomson, Jenny, Bradshaw, Kirsty, Dixit, Abhijit, Eason, Jacqueline, Haines, Rebecca, Harrison, Rachel, Mutch, Stacey, Sarkar, Ajoy, Searle, Claire, Shannon, Nora, Sharif, Abid, Suri, Mohnish, Vasudevan, Pradeep, Canham, Natalie, Ellis, Ian, Greenhalgh, Lynn, Howard, Emma, Stinton, Victoria, Swale, Andrew, Weber, Astrid, Banka, Siddharth, Breen, Catherine, Briggs, Tracy, Burkitt-Wright, Emma, Chandler, Kate, Clayton-Smith, Jill, Donnai, Dian, Douzgou, Sofia, Gaunt, Lorraine, Jones, Elizabeth, Kerr, Bronwyn, Langley, Claire, Metcalfe, Kay, Smith, Audrey, Wright, Ronnie, Bourn, David, Burn, John, Fisher, Richard, Hellens, Steve, Henderson, Alex, Montgomery, Tara, Splitt, Miranda, Straub, Volker, Wright, Michael, Zwolinski, Simon, Allen, Zoe, Bernhard, Birgitta, Brady, Angela, Brooks, Claire, Busby, Louise, Clowes, Virginia, Ghali, Neeti, Holder, Susan, Ibitoye, Rita, Wakeling, Emma, Blair, Edward, Carmichael, Jenny, Cilliers, Deirdre, Clasper, Susan, Gibbons, Richard, Kini, Usha, Lester, Tracy, Nemeth, Andrea, Poulton, Joanna, Price, Sue, Shears, Debbie, Stewart, Helen, Wilkie, Andrew, Albaba, Shadi, Baker, Duncan, Balasubramanian, Meena, Johnson, Diana, Parker, Michael, Quarrell, Oliver, Stewart, Alison, Willoughby, Josh, Crosby, Charlene, Elmslie, Frances, Homfray, Tessa, Jin, Huilin, Lahiri, Nayana, Mansour, Sahar, Marks, Karen, McEntagart, Meriel, Saggar, Anand, Tatton-Brown, Kate, Butler, Rachel, Clarke, Angus, Corrin, Sian, Fry, Andrew, Kamath, Arveen, McCann, Emma, Mugalaasi, Hood, Pottinger, Caroline, Procter, Annie, Sampson, Julian, Sansbury, Francis, Varghese, Vinod, Baralle, Diana, Callaway, Alison, Cassidy, Emma J., Daniels, Stacey, Douglas, Andrew, Foulds, Nicola, Hunt, David, Kharbanda, Mira, Lachlan, Katherine, Mercer, Catherine, Side, Lucy, Temple, I. Karen, Wellesley, Diana, Ambrose, J.C., Arumugam, P., Baple, E.L., Bleda, M., Boardman-Pretty, F., Boissiere, J.M., Boustred, C.R., Caulfield, M.J., Chan, G.C., Craig, C.E.H., Daugherty, L.C., de Burca, A., Devereau, A., Elgar, G., Foulger, R.E., Fowler, T., FurióTarí, P., Hackett, J.M., Halai, D., Hamblin, A., Henderson, S., Holman, J.E., Hubbard, T.J.P., Ibáñez, K., Jackson, R., Jones, L.J., Kasperaviciute, D., Kayikci, M., Lahnstein, L., Lawson, K., Leigh, S.E.A., Leong, I.U.S., Lopez, F.J., MaleadyCrowe, F., Mason, J., McDonagh, E.M., Moutsianas, L., Mueller, M., Murugaesu, N., Need, A.C., Odhams, C.A., Patch, C., Perez-Gil, D., Polychronopoulos, D., Pullinger, J., Rahim, T., Rendon, A., Riesgo-Ferreiro, P., Rogers, T., Ryten, M., Savage, K., Sawant, K., Scott, R.H., Siddiq, A., Sieghart, A., Smedley, D., Smith, K.R., Sosinsky, A., Spooner, W., Stevens, H.E., Stuckey, A., Sultana, R., Thomas, E.R.A., Thompson, S.R., Tucci, A., Walsh, E., Watters, S.A., Welland, M.J., Williams, E., Witkowska, K., Acosta, Maria T., Adam, Margaret, Adams, David R., Agrawal, Pankaj B., Alejandro, Mercedes E., Alvey, Justin, Amendola, Laura, Andrews, Ashley, Ashley, Euan A., Azamian, Mahshid S., Bacino, Carlos A., Bademci, Guney, Baker, Eva, Balasubramanyam, Ashok, Baldridge, Dustin, Bale, Jim, Bamshad, Michael, Barbouth, Deborah, Bayrak-Toydemir, Pinar, Beck, Anita, Beggs, Alan H., Behrens, Edward, Bejerano, Gill, Bennet, Jimmy, Berg-Rood, Beverly, Bernstein, Jonathan A., Berry, Gerard T., Bican, Anna, Bivona, Stephanie, Blue, Elizabeth, Bohnsack, John, Bonnenmann, Carsten, Bonner, Devon, Botto, Lorenzo, Boyd, Brenna, Briere, Lauren C., Brokamp, Elly, Brown, Gabrielle, Burke, Elizabeth A., Burrage, Lindsay C., Butte, Manish J., Byers, Peter, Byrd, William E., Carey, John, Carrasquillo, Olveen, Peter Chang, Ta Chen, Chanprasert, Sirisak, Chao, Hsiao-Tuan, Clark, Gary D., Coakley, Terra R., Cobban, Laurel A., Cogan, Joy D., Coggins, Matthew, Cole, F. Sessions, Colley, Heather A., Cooper, Cynthia M., Craigen, William J., Crouse, Andrew B., Cunningham, Michael, D'Souza, Precilla, Dai, Hongzheng, Dasari, Surendra, Davids, Mariska, Dayal, Jyoti G., Deardorff, Matthew, Dell'Angelica, Esteban C., Dhar, Shweta U., Dipple, Katrina, Doherty, Daniel, Dorrani, Naghmeh, Douine, Emilie D., Draper, David D., Duncan, Laura, Earl, Dawn, Eckstein, David J., Emrick, Lisa T., Eng, Christine M., Esteves, Cecilia, Estwick, Tyra, Falk, Marni, Fernandez, Liliana, Ferreira, Carlos, Fieg, Elizabeth L., Findley, Laurie C., Fisher, Paul G., Fogel, Brent L., Forghani, Irman, Fresard, Laure, Gahl, William A., Glass, Ian, Godfrey, Rena A., Golden-Grant, Katie, Goldman, Alica M., Goldstein, David B., Grajewski, Alana, Groden, Catherine A., Gropman, Andrea L., Gutierrez, Irma, Hahn, Sihoun, Hamid, Rizwan, Hanchard, Neil A., Hassey, Kelly, Hayes, Nichole, High, Frances, Hing, Anne, Hisama, Fuki M., Holm, Ingrid A., Hom, Jason, Horike-Pyne, Martha, Huang, Alden, Huang, Yong, Isasi, Rosario, Jamal, Fariha, Jarvik, Gail P., Jarvik, Jeffrey, Jayadev, Suman, Johnston, Jean M., Karaviti, Lefkothea, Kelley, Emily G., Kennedy, Jennifer, Kiley, Dana, Kohane, Isaac S., Kohler, Jennefer N., Krakow, Deborah, Krasnewich, Donna M., Kravets, Elijah, Korrick, Susan, Koziura, Mary, Krier, Joel B., Lalani, Seema R., Lam, Byron, Lam, Christina, Lanpher, Brendan C., Lanza, Ian R., Lau, C. Christopher, LeBlanc, Kimberly, Lee, Brendan H., Lee, Hane, Levitt, Roy, Lewis, Richard A., Lincoln, Sharyn A., Liu, Pengfei, Liu, Xue Zhong, Longo, Nicola, Loo, Sandra K., Loscalzo, Joseph, Maas, Richard L., Macnamara, Ellen F., MacRae, Calum A., Maduro, Valerie V., Majcherska, Marta M., Mak, Bryan, Malicdan, May Christine V., Mamounas, Laura A., Manolio, Teri A., Mao, Rong, Maravilla, Kenneth, Markello, Thomas C., Marom, Ronit, Marth, Gabor, Martin, Beth A., Martin, Martin G., Martínez-Agosto, Julian A., Marwaha, Shruti, McCauley, Jacob, McCormack, Colleen E., McCray, Alexa T., McGee, Elisabeth, Mefford, Heather, Merritt, J. Lawrence, Might, Matthew, Mirzaa, Ghayda, Morava, Eva, Moretti, Paolo M., Morimoto, Marie, Mulvihill, John J., Murdock, David R., Nakano-Okuno, Mariko, Nath, Avi, Nelson, Stan F., Newman, John H., Nicholas, Sarah K., Nickerson, Deborah, Nieves-Rodriguez, Shirley, Novacic, Donna, Oglesbee, Devin, Orengo, James P., Pace, Laura, Pak, Stephen, Pallais, J. Carl, Papp, Jeanette C., Parker, Neil H., Phillips, John A., Posey, Jennifer E., Potocki, Lorraine, Pusey, Barbara N., Quinlan, Aaron, Raskind, Wendy, Raja, Archana N., Rao, Deepak A., Renteria, Genecee, Reuter, Chloe M., Rives, Lynette, Robertson, Amy K., Rodan, Lance H., Rosenfeld, Jill A., Rosenwasser, Natalie, Ruzhnikov, Maura, Sacco, Ralph, Sampson, Jacinda B., Samson, Susan L., Saporta, Mario, Scott, C. Ron, Schaechter, Judy, Schedl, Timothy, Scott, Daryl A., Sharma, Prashant, Shin, Jimann, Signer, Rebecca, Sillari, Catherine H., Silverman, Edwin K., Sinsheimer, Janet S., Sisco, Kathy, Smith, Edward C., Smith, Kevin S., Solem, Emily, Solnica-Krezel, Lilianna, Stoler, Joan M., Stong, Nicholas, Sullivan, Jennifer A., Sun, Angela, Sutton, Shirley, Sweetser, David A., Sybert, Virginia, Tabor, Holly K., Tamburro, Cecelia P., Tekin, Mustafa, Telischi, Fred, Thorson, Willa, Tifft, Cynthia J., Toro, Camilo, Tran, Alyssa A., Tucker, Brianna M., Urv, Tiina K., Vanderver, Adeline, Velinder, Matt, Viskochil, Dave, Vogel, Tiphanie P., Wahl, Colleen E., Wallace, Stephanie, Walley, Nicole M., Walsh, Chris A., Walker, Melissa, Wambach, Jennifer, Wan, Jijun, Wang, Lee-Kai, Wangler, Michael F., Ward, Patricia A., Wegner, Daniel, Wener, Mark, Wenger, Tara, Perry, Katherine Wesseling, Westerfield, Monte, Wheeler, Matthew T., Whitlock, Jordan, Wolfe, Lynne A., Woods, Jeremy D., Yamamoto, Shinya, Yang, John, Yu, Guoyun, Zastrow, Diane B., Zhao, Chunli, Zuchner, Stephan, Jeffries, Lauren, Mis, Emily K., McWalter, Kirsty, Donkervoort, Sandra, Brodsky, Nina N., Carpier, Jean-Marie, Ji, Weizhen, Ionita, Cristian, Roy, Bhaskar, Morrow, Jon S., Darbinyan, Armine, Iyer, Krishna, Aul, Ritu B., Chao, Katherine R., Cobbold, Laura, Cohen, Stacey, Custodio, Helena M., Drummond-Borg, Margaret, Finanger, Erika, Hainline, Bryan E., Helbig, Ingo, Hewson, Stacy, Hu, Ying, Jackson, Adam, Konstantino, Monica, Leach, Meganne E., McCormick, David, Nelson, Stanley, Nguyen, Joanne, Nugent, Kimberly, Ortega, Lucy, Goodkin, Howard P., Roeder, Elizabeth, Roy, Sani, Sapp, Katie, Saade, Dimah, Sisodiya, Sanjay M., Stals, Karen, Towner, Shelley, Wilson, William, Khokha, Mustafa K., Bönnemann, Carsten G., Lucas, Carrie L., and Lakhani, Saquib A.

Published
2024
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11. On explicit estimates for $S(t)$, $S_1(t)$, and $\zeta(1/2+\mathrm{i}t)$ under the Riemann Hypothesis

Author

Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11M26
Abstract

Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S(t)$, $S_1(t)$, and $\zeta\left(1/2+\mathrm{i}t\right)$ while comparing them with recently proven unconditional ones. As a corollary we obtain a conditional explicit bound on gaps between consecutive zeros of the Riemann zeta-function., Comment: 21 pages

Published
2020
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12. Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function

Author

Simonič, A., Trudgian, T., and Turnage-Butterbaugh, C. L.

Subjects
Mathematics - Number Theory, 11M06, 11M26
Abstract

We make explicit an argument of Heath-Brown concerning large and small gaps between nontrivial zeroes of the Riemann zeta-function, $\zeta(s)$. In particular, we provide the first unconditional results on gaps (large and small) which hold for a positive proportion of zeroes. To do this we prove explicit bounds on the second and fourth power moments of $S(t+h)-S(t)$, where $S(t)$ denotes the argument of $\zeta(s)$ on the critical line and $h \ll 1 / \log T$. We also use these moments to prove explicit results on the density of the nontrivial zeroes of $\zeta(s)$ of a given multiplicity.

Published
2020

13. Quasimodularity of the $k$th Residual Cranks

Author

Morrill, Thomas and Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11P81, 05A17
Abstract

We establish quasimodularity for a family of residual crank generating functions defined on overpartitions. We also show that the second moments of these $k$th residual cranks admit a combinatoric interpretation as weighted overpartition counts.

Published
2020

14. A note on a straight gravity tunnel through a rotating body

Author

Simonič, Aleksander

Subjects
Physics - Popular Physics
Abstract

It is well-known that the straight gravity tunnel between any two different positions on a non-rotating Earth, which has uniform density, is traversable, i.e., an object initially at rest will reach its destination through the gravity tunnel in both directions. Moreover, the time taken to fall is always constant. These facts are no longer true if rotation is allowed. The aim of this note is to derive the necessary and sufficient condition for traversability of straight gravity tunnels through a rotating physical body with spherically symmetric gravitational field. Fall-through times are expressed in a closed form for linear and constant gravitational fields. In conclusion, these models are compared to numerically obtained data using the internal structure of the Earth.

Published
2020
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16. Explicit zero density estimate for the Riemann zeta-function near the critical line

Author

Simonič, Aleksander

Subjects
Mathematics - Number Theory
Abstract

In 1946, A. Selberg proved $N(\sigma,T) \ll T^{1-\frac{1}{4} \left(\sigma-\frac{1}{2}\right)} \log{T}$ where $N(\sigma,T)$ is the number of nontrivial zeros $\rho$ of the Riemann zeta-function with $\Re\{\rho\}>\sigma$ and $0<\Im\{\rho\}\leq T$. We provide an explicit version of this estimate, together with an explicit approximate functional equation and an explicit upper bound for the second power moment of the zeta-function on the critical line., Comment: 35 pages, 1 figure, 3 tables

Published
2019

17. Platonic configurations of points and lines

Author

Kovič, Jurij and Simonič, Aleksander

Subjects
Mathematics - Combinatorics, 51A20, 51M20
Abstract

We present some methods for constructing connected spatial geometric configurations $(p_{q}, n_{k})$ of points and lines, preserved by the same rotations (and reflections) of Euclidean space $E^{3}$ as the chosen Platonic solid. In this paper we are primarily interested in balanced configurations $(n_{3}), (n_{4})$ and $(n_{5})$, but also in unbalanced configurations $(p_{3},n_{4}), (p_{3}, n_{5})$ and $(p_{4}, n_{5})$.

Published
2019

18. On Littlewood's proof of the prime number theorem

Author

Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11N05, 42A75
Abstract

In this note we examine Littlewood's proof of the prime number theorem. We show that this can be extended to provide an equivalence between the prime number theorem and the non-vanishing of Riemann's zeta-function on the one-line. Our approach goes through the theory of almost periodic functions and is self-contained.

Published
2019

21. Publish-and-Flourish: decentralized co-creation and curation of scholarly content

Author

Duh, Emilija Stojmenova, Duh, Andrej, Droftina, Uroš, Kos, Tim, Duh, Urban, Korošak, Tanja Simonič, and Korošak, Dean

Subjects
Computer Science - Distributed, Parallel, and Cluster Computing, Computer Science - Digital Libraries
Abstract

Scholarly communication is today immersed in publish or perish culture that propels noncooperative behaviour in the sense of strategic games played by researchers. Here we introduce and describe a blockchain based platform for decentralized scholarly communication. The design of the platform rests on community driven publishing reviewing processes and implements incentives that promote cooperative user behaviour. Key to achieve cooperation in blockchain based scholarly communication is to transform a static research paper into a modifiable research paper under continuous peer review process. We describe and discuss the implementation of a modifiable research paper as a smart contract on the blockchain.

Published
2018

23. CommAI: Evaluating the first steps towards a useful general AI

Author

Baroni, Marco, Joulin, Armand, Jabri, Allan, Kruszewski, Germàn, Lazaridou, Angeliki, Simonic, Klemen, and Mikolov, Tomas

Subjects
Computer Science - Learning, Computer Science - Artificial Intelligence, Computer Science - Computation and Language
Abstract

With machine learning successfully applied to new daunting problems almost every day, general AI starts looking like an attainable goal. However, most current research focuses instead on important but narrow applications, such as image classification or machine translation. We believe this to be largely due to the lack of objective ways to measure progress towards broad machine intelligence. In order to fill this gap, we propose here a set of concrete desiderata for general AI, together with a platform to test machines on how well they satisfy such desiderata, while keeping all further complexities to a minimum., Comment: Published in ICLR 2017 Workshop Track

Published
2017

24. Modular Real-Time System for Upper-Body Motion Imitation on Humanoid Robot Talos

Author

Savevska, Kristina, Simonič, Mihael, Ude, Aleš, Ceccarelli, Marco, Series Editor, Agrawal, Sunil K., Advisory Editor, Corves, Burkhard, Advisory Editor, Glazunov, Victor, Advisory Editor, Hernández, Alfonso, Advisory Editor, Huang, Tian, Advisory Editor, Jauregui Correa, Juan Carlos, Advisory Editor, Takeda, Yukio, Advisory Editor, Zeghloul, Saïd, editor, Laribi, Med Amine, editor, and Sandoval, Juan, editor

Published
2021
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26. Generalization Based Database Acquisition for Robot Learning in Reduced Space

Author

Lončarević, Zvezdan, Pahič, Rok, Simonič, Mihael, Ude, Aleš, Gams, Andrej, Ceccarelli, Marco, Series Editor, Hernandez, Alfonso, Editorial Board Member, Huang, Tian, Editorial Board Member, Takeda, Yukio, Editorial Board Member, Corves, Burkhard, Editorial Board Member, Agrawal, Sunil, Editorial Board Member, Zeghloul, Saïd, editor, Laribi, Med Amine, editor, and Sandoval Arevalo, Juan Sebastian, editor

Published
2020
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27. Reduction of Trajectory Encoding Data Using a Deep Autoencoder Network: Robotic Throwing

Author

Lončarević, Zvezdan, Pahič, Rok, Simonič, Mihael, Ude, Aleš, Gams, Andrej, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Berns, Karsten, editor, and Görges, Daniel, editor

Published
2020
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28. Lehmer pairs and derivatives of Hardy's $Z$-function

Author

Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11M06, 11M26
Abstract

Occurrences of very close zeros of the Riemann zeta function are strongly connected with Lehmer pairs and with the Riemann Hypothesis. The aim of the present note is to derive a condition for a pair of consecutive simple zeros of the $\zeta$-function to be a Lehmer pair in terms of derivatives of Hardy's $Z$-function. Furthermore, we connect Newman's conjecture with stationary points of the $Z$-function, and present some numerical results., Comment: 8 pages

Published
2016

29. Elementary approach to the Hartogs extension theorem

Author

Simonič, Aleksander

Subjects
Mathematics - Complex Variables, 32D15, 30E20
Abstract

In this paper we present a proof of Hartogs' extension theorem, following T. Sobieszek's paper from 2003. Hartogs' theorem provides a large class of domains where holomorphic functions have analytic continuation to larger domains, and is "a several complex variables theorem" in nature because its conclusion is false in the complex plane. Sobieszek's proof is quite remarkable because he uses, stated in his paper without proofs, only higher-dimensional identity principle for holomorphic functions and Cauchy's integral formula for compact sets. We proved this two theorems here, making this exposition self-contained. The only background required is an undergraduate course in real and complex analysis and in point-set topology.

Published
2016

32. The Ahlfors lemma and Picard's theorems

Author

Simonič, Aleksander

Subjects
Mathematics - Complex Variables, 30C80, 30F45
Abstract

The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings, including the celebrated Picard's theorems. The article concludes with a brief insight into the theory of Kobayashi hyperbolic complex manifolds., Comment: 18 pages, 2 figures

Published
2015

33. Antimicrobial Activity of Olive Leaf Extract to Oral Candida Isolates.

Author

Kinkela Devčić, Maja, Pasković, Igor, Kovač, Zoran, Knežević, Petra Tariba, Morelato, Luka, Glažar, Irena, and Simonić-Kocijan, Sunčana

Subjects
OLIVE leaves, ANTI-infective agents, ORAL diseases, CANDIDA, NYSTATIN, ANTIFUNGAL agents
Abstract

Objectives: The aim of this study was to determine the antifungal activity of olive leaf extract (OLE) and the synergistic effect of standard antifungal therapy and OLE against clinical oral Candida species' isolates. Materials and Method: The susceptibility of 60 clinical isolates of the Candida species (36 C. albicans, 16 C. krusei, 5 C. glabrata and 3 C. tropicalis) was tested with four concentrations of OLE (60 µg/µL, 120 µg/µL, 240 µg/µL and 333 µg/µL) and the synergistic effect of standard antifungal therapy and OLE (miconazole (MIC) + 333 µg/µL OLE and nystatin (NYS) + 333 µg/µL OLE). The antimicrobial activity was tested using the disk diffusion method. Results: All concentrations (60 µg/µL, 120 µg/µL, 240 µg/µL and 333 µg/µL) of OLE showed a statistically significant effect on all Candida species compared to the control (DMSO) except for the lowest concentration (60 µg/µL) tested on C. glabrata. There was a dose-dependent effect of OLE on tested samples. Concentrations of 240 µg/µL and 333 µg/µL showed statistically significant higher antifungal activity compared to the lowest concentration of 60 µg/µL. No statistically significant synergistic effect of OLE and standard antifungal therapy was found compared with standard therapy alone. Conclusions: The results of this study present the significant antimicrobial effect of OLE against all tested Candida species except for the lowest concentration on C. glabrata. Increasing the concentration of OLE also increases its effect on Candida species. This indicates the possible potential effect of OLE in the treatment of Candida-related oral diseases. [ABSTRACT FROM AUTHOR]

Published
2024
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34. P2Y2 Receptors Mediate Masseter Muscle Mechanical Hypersensitivity in Rats

Author

Tariba Knežević P, Vukman R, Uhač M, Illeš D, Kovačević Pavičić D, and Simonić-Kocijan S

Subjects
facial pain, masticatory muscles, temporomandibular disorders, trigeminal ganglion, Medicine (General), R5-920
Abstract

Petra Tariba Knežević,1,2 Robert Vukman,1,2 Mia Uhač,3 Davor Illeš,4 Daniela Kovačević Pavičić,1,2 Sunčana Simonić-Kocijan1,2 1Department of Prosthodontics, Faculty of Dental Medicine, University of Rijeka, Rijeka, Croatia; 2Department of Prosthodontics, Clinic of Dental Medicine, Clinical Hospital Center Rijeka, Rijeka, Croatia; 3Department of Orthodontics, Clinic of Dental Medicine, Clinical Hospital Center Rijeka, Rijeka, Croatia; 4Department of Removable Prosthodontics, School of Dental Medicine, University of Zagreb, Zagreb, CroatiaCorrespondence: Sunčana Simonić-KocijanDepartment of Prosthodontics, Faculty of Dental Medicine, University of Rijeka, Krešimirova 40, Rijeka 51000, CroatiaTel +385 51 345 633Fax +385 51 345 630Email suncanask@uniri.hrPurpose: P2Y2 receptors (P2Y2Rs) are among the various receptors that play an important role in nociception. The goal of this research was to investigate possible P2Y2R expression changes in the trigeminal ganglion (TRG) in bilateral masseter muscle (MM) hypersensitivity following unilateral MM inflammation. The impact of unilateral intramasseteric administration of P2Y2R antagonist on bilateral MM hypersensitivity was also explored.Materials and Methods: Bilateral MM hypersensitivity was provoked by unilateral intramasseteric injection of complete Freund’s adjuvant (CFA). The head withdrawal threshold (HWT) was assessed bilaterally 4 days later. Bilateral TRG and MM isolation were followed, and quantitative real-time polymerase chain reaction (qRT-PCR) and histopathological analysis were carried out on these tissues, respectively. The involvement of P2Y2Rs in nocifensive behavior was evaluated by administering two doses of P2Y2R antagonist AR-C118925 (0.2 or 1 mg/100 μL) in inflamed MM 4 days post-CFA administration. Bilateral HWT was assessed at different time points following antagonist injection.Results: qRT-PCR analysis demonstrated P2Y2R up-regulation in TRG ipsilateral to the site of CFA administration. Compared to the controls, both doses of AR-C118925 injected ipsilateral to the TRG increased the bilateral HWT at 30, 60, 90, and 120 minutes after antagonist administration.Conclusion: The findings suggest that P2Y2Rs may affect MM inflammatory hypersensitivity owing to its up-regulation in the TRG in MM inflammatory pain states.Keywords: facial pain, masticatory muscles, temporomandibular disorders, trigeminal ganglion

Published
2020

41. Revitalizing Rural Tourism: A Croatian Case Study in Sustainable Practices.

Author

Funduk, Marina, Biondić, Ivana, and Simonić, Abra Lea

Abstract

Dubrovnik-Neretva County, renowned for the City of Dubrovnik, grapples with tourism challenges affecting its UNESCO-listed Old City. This study advocates for promoting less-explored inland areas to ease the strain on the heritage site and alleviate coastal tourist pressure. By diversifying tourism and supporting sustainable rural development, the region can spur economic growth, foster local businesses, and improve infrastructure through EU and national funding. The research explores financial investments in less-developed areas, emphasizing sustainable tourism practices for socio-economic and environmental benefits. The analysis highlights the project's positive impact on sustainable tourism development inland, preserving natural heritage, and fostering economic benefits for local communities. According to the cost–benefit analysis, the proposed idea outperforms all alternatives with new attractions and enhanced infrastructure, contributing to overall municipal growth. External funding is crucial for viability, with a negative net income until 2040, offset by municipal support. Economic indicators justify social and economic benefits, emphasizing project resilience. The active tourism centre project, emphasizing eco-friendly outdoor activities, highlights the role of cost–benefit analysis in rural tourism infrastructure investment, recommending external funding for success. [ABSTRACT FROM AUTHOR]

Published
2024
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42. Phenolic Potential of Olive Leaves from Different Istrian Cultivars in Croatia

Author

Polić Pasković, Marija, primary, Vidović, Nikolina, additional, Lukić, Igor, additional, Žurga, Paula, additional, Majetić Germek, Valerija, additional, Goreta Ban, Smiljana, additional, Kos, Tomislav, additional, Čoga, Lepomir, additional, Tomljanović, Tea, additional, Simonić-Kocijan, Sunčana, additional, Ban, Dean, additional, Godena, Sara, additional, and Pasković, Igor, additional

Published
2023
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45. Development of an Interactive Application for Learning Medical Procedures and Clinical Decision Making

Author

Bloice, Marcus, Simonic, Klaus-Martin, Kreuzthaler, Markus, Holzinger, Andreas, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Holzinger, Andreas, editor, and Simonic, Klaus-Martin, editor

Published
2011
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46. Navigating through Very Large Sets of Medical Records: An Information Retrieval Evaluation Architecture for Non-standardized Text

Author

Kreuzthaler, Markus, Bloice, Marcus, Simonic, Klaus-Martin, Holzinger, Andreas, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Holzinger, Andreas, editor, and Simonic, Klaus-Martin, editor

Published
2011
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47. Phenolic Potential of Olive Leaves from Different Istrian Cultivars in Croatia

Author

Marija Polić Pasković, Nikolina Vidović, Igor Lukić, Paula Žurga, Valerija Majetić Germek, Smiljana Goreta Ban, Tomislav Kos, Lepomir Čoga, Tea Tomljanović, Sunčana Simonić-Kocijan, Dean Ban, Sara Godena, and Igor Pasković

Subjects
BIOTECHNICAL SCIENCES. Interdisciplinary Technical Sciences, Olea europaea L, ‘Leccino’, oleuropein, ‘Buža’, Plant Science, phenols, Horticulture, BIOTEHNIČKE ZNANOSTI. Interdisciplinarne biotehničke znanosti, minerals
Abstract

For the first time the effects of different sampling periods and their interaction with five major autochthonous Croatian Istrian olive cultivars and the Italian cultivar ‘Leccino’ on the quantity and composition of olive leaf phenolic compounds and mineral nutrients were investigated. For that purpose, olive leaves were sampled in two collecting periods, in October and March, coinciding with the harvesting and pruning periods, respectively. All selected cultivars had a higher oleuropein leaf content in the pruning collecting period, with the highest levels noted for the ‘Leccino’ and ‘Buža’ cultivars. Cultivar significantly affected almost all the investigated phenols, with higher concentrations of these valuable compounds in the pruning than in the harvesting period. Differences observed in leaf mineral composition were closely related to the differences in phenolic profiles and were significantly affected by genotype. Some of the studied mineral nutrients, such as P, Cu and B, were found to be significantly correlated with the most abundant olive leaf phenolic compounds, oleuropein and verbascoside.

Published
2023
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50. ANTIFUNGAL ACTIVITY OF OLIVE LEAF EXTRACT ON ORAL CANDIDA ISOLATES

Author

Kinkela Devčić Maja, Simonić-Kocijan Suncana, Pasković Igor, Vučinić Davor, Morelato Luka, Sever Ella

Subjects
Antifungal activity, Candida, Candida albicans, Olive leaf extract
Abstract

Introduction: Candida species (Candida spp.) is a part of the normal flora in the oral cavity. Candida may cause various forms of infections, from superficial to systemic conditions. With the increasing use of antifungal agents and a growing number of resistant strains, many researchers are working to find new potential herbal therapeutics that may be a safer alternative in treatment. Among natural products, Olive leaf extract (OLE) is a promising therapeutic tool for the treatment of oral infections due to its antimicrobial activity against a large number of pathogenic microorganisms. Aim: The aim of this study was to determine the antifungal activity of OLE against clinical isolates of Candida spp. Materials and Methods: Using the disc diffusion method, we tested the sensitivity of 15 clinical oral isolates of Candida spp. (11 C.albicans, 3 C. krusei, and 1 C. tropicalis) to four concentrations of OLE (7.5 µg/µL, 15 µg/µL, 30 µg/ µL and 60 µg/µL). Results: All tested concentrations of OLE showed a statistically significantly higher antifungal effect against Candida spp. compared to the control (DMSO). There was a concentration- dependent effect of OLE on the tested samples. Concentrations of 60 µg/µl and 30 µg/µl had statistically significantly higher antifungal activity compared to concentrations of 15 µg/µl and 7.5 µg/µl and a concentration of 30 µg/µl compared to the lowest tested concentration of 7.5 µg/µl. Conclusion: OLE could be a potential drug in the treatment of oral diseases caused by Candida.

Published
2023

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