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3,875 results on '"A. Hynd"'

1. On a Hardy-Morrey inequality

Author

Hynd, Ryan, Larson, Simon, and Lindgren, Erik

Subjects
Mathematics - Analysis of PDEs, Mathematics - Functional Analysis, 26D10, 46E35, 35P30
Abstract

Morrey's classical inequality implies the H\"older continuity of a function whose gradient is sufficiently integrable. Another consequence is the Hardy-type inequality $$ \lambda\biggl\|\frac{u}{d_\Omega^{1-n/p}}\biggr\|_{\infty}^p\le \int_\Omega |Du|^p \,dx $$ for any open set $\Omega\subsetneq \mathbb{R}^n$. This inequality is valid for functions supported in $\Omega$ and with $\lambda$ a positive constant independent of $u$. The crucial hypothesis is that the exponent $p$ exceeds the dimension $n$. This paper aims to develop a basic theory for this inequality and the associated variational problem. In particular, we study the relationship between the geometry of $\Omega$, sharp constants, and the existence of a nontrivial $u$ which saturates the inequality.

Published
2024

2. Asymptotics of the Sticky Particles evolution

Author

Hynd, Ryan and Tudorascu, Adrian

Subjects
Mathematics - Analysis of PDEs
Abstract

We study the long-time asymptotic behavior of the Sticky Particles dynamics on the real line. The time average of the Sticky Particles Lagrangian map has a limit which arises as a general property of projections onto closed convex cones in Hilbert spaces. More notably, we prove that the map itself has an asymptotic limit in the case where the Sticky Particles dynamics is confined to a compact set.

Published
2023

3. The perimeter and volume of a Reuleaux polyhedron

Author

Hynd, Ryan

Subjects
Mathematics - Metric Geometry
Abstract

A ball polyhedron is the intersection of a finite number of closed balls in $\mathbb{R}^3$ with the same radius. In this note, we study ball polyhedra in which the set of centers defining the balls have the maximum possible number of diametric pairs. We explain how to compute the perimeter and volume of these shapes by employing the Gauss-Bonnet theorem and another integral formula. In addition, we show how to adapt this method to approximate the volume of Meissner polyhedra, which are constant width bodies constructed from ball polyhedra.

Published
2023

4. On the uniqueness of eigenfunctions for the vectorial $p$-Laplacian

Author

Hynd, Ryan, Kawohl, Bernd, and Lindqvist, Peter

Subjects
Mathematics - Analysis of PDEs
Abstract

We study a non-linear eigenvalue problem for vector-valued eigenfunctions and give a succinct uniqueness proof for minimizers of the associated Rayleigh quotient.

Published
2023

5. Decay of extremals of Morrey's inequality

Author

Hynd, Ryan, Larson, Simon, and Lindgren, Erik

Subjects
Mathematics - Analysis of PDEs, 35B65, 35J70
Abstract

We study the decay (at infinity) of extremals of Morrey's inequality in $\mathbb{R}^n$. These are functions satisfying $$ \displaystyle \sup_{x\neq y}\frac{|u(x)-u(y)|}{|x-y|^{1-\frac{n}{p}}}= C(p,n)\|\nabla u\|_{L^p(\mathbb{R}^n)} , $$ where $p>n$ and $C(p,n)$ is the optimal constant in Morrey's inequality. We prove that if $n \geq 2$ then any extremal has a power decay of order $\beta$ for any $$ \beta<-\frac13+\frac{2}{3(p-1)}+\sqrt{\left(-\frac13+\frac{2}{3(p-1)}\right)^2+\frac13}. $$

Published
2023

6. The density of Meissner polyhedra

Author

Hynd, Ryan

Subjects
Mathematics - Metric Geometry
Abstract

We consider Meissner polyhedra in $\mathbb{R}^3$. These are constant width bodies whose boundaries consist of pieces of spheres and spindle tori. We define these shapes by taking appropriate intersections of congruent balls and show that they are dense within the space of constant width bodies in the Hausdorff topology. This density assertion was essentially proved by Sallee. However, we offer a modern viewpoint taking into consideration the recent progress in understanding ball polyhedra and in constructing constant width bodies based on these shapes.

Published
2023

7. The Blaschke-Lebesgue theorem revisited

Author

Hynd, Ryan

Subjects
Mathematics - Metric Geometry, Mathematics - Optimization and Control
Abstract

We revisit a classic proof of the Blaschke-Lebesgue theorem. It is based on the support function of a convex curve and the approximation of constant width curves by Reuleaux polygons.

Published
2023

11. Digital Linguistic Landscapes: Unveiling Youth Code-Switching in Computer-Mediated Communication

Author

Hynd KAID SLIMANE

Subjects
Language and Literature
Abstract

Abstract: In the dynamic digital landscape, the realm of youth communication has evolved into a captivating playground where the intricate dynamics of code-switching and language innovation manifest, characterized by the use of diverse languages or linguistic varieties. This paper seeks to delve into the underlying motivations driving code-switching and linguistic innovation among EFL learners, while concurrently scrutinizing the socio-cultural factors that influence these linguistic practices. Furthermore, it seeks to examine the profound impact exerted by technology and social media on the linguistic repertoire and communicative behaviors of the youth. Methodologically grounded in a mixed-method approach, which incorporates both quantitative and qualitative instruments for data collection, such as questionnaires and interviews, this study navigates through the linguistic landscape occupied by first-year English students at Tlemcen University(Algeria). Through systematic analysis and interpretation, the findings elucidate the emergence of a new form of written language within computer-mediated communication platforms, thereby shedding light on the youth’s' positive attitudes toward linguistic innovations. Moreover, the findings underscore the active engagement of these learners within the digital field, highlighting their adeptness in navigating the complexities of digital communication. In sum, this research contributes not only to the discourse on language variation and digital communication but also provides valuable insights into the intricate interplay between language, technology, and culture within educational contexts. Keywords: Attitudes, code-switching, computer-mediated communication, language innovation

Published
2024
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12. Evolution of mixed strategies in monotone games

Author

Hynd, Ryan

Subjects
Mathematics - Functional Analysis, Mathematics - Optimization and Control
Abstract

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which arise in the large player limit of symmetric noncooperative games. In this setting, we will additionally show that the approximation of mean field equilibria is possible under a suitable monotonicity hypothesis.

Published
2022

14. Dialect Conflict and Identity Issues in Tlemcen Speech Community

Author

Slimane-Mahdad, Hynd Kaid

Abstract

The present article aims at serving as a reference work in the field of sociolinguistics. It also provides a concise summary of the sociolinguistic situation in an Algerian stereotyped speech community named Tlemcen. In addition, it sheds light on the status of its dialect, which most people consider as one of the most distinguished and stigmatized dialects in the Algerian society. This article also discusses the effect of bi-dialectalism on Tlemcen native speakers' identity. To reach the aim of the study, the following hypotheses are formulated: First, the widespread of the rural variety in Tlemcen speech community may affect the social and cultural identity of Tlemcenians. Second, Tlemcen native speakers show negative attitudes towards the use of the rural variety, especially among females. Yet, the mixed variety is gradually gaining a pleasant status in Tlemcen speech community and its adoption is rather acceptable. For the sake of collecting information about the issue, the researcher has used both qualitative and quantitative instruments. The research findings reveal that dialect shift has negative effects on the social and cultural identity of Tlemcen native speakers which may probably lead to an identity crisis among them. In addition, we have noticed that another variety, the mixed one (a mixture of urban and rural varieties), is progressively displacing the urban one, and may undoubtedly affect the maintenance of Tlemcen dialect.

Published
2019

15. A doubly monotone flow for constant width bodies in $\mathbb{R}^3$

Author

Hynd, Ryan

Subjects
Mathematics - Functional Analysis
Abstract

We introduce a flow in the space of constant width bodies in three-dimensional Euclidean space that simultaneously increases the volume and decreases the circumradius of the shape as time increases. Starting from any initial constant width figure, we show that the flow exists for all positive times and converges to a closed ball as time tends to plus infinity. We also anticipate that this flow is interesting to study for negative times and that it would provide a mechanism to decrease the volume and increase the circumradius of a constant width body.

Published
2021

16. Listeria monocytogenes-associated spontaneous bacterial peritonitis in France: a nationwide observational study of 208 cases

Author

Abdou, Mohamed, Abdulhai, Ayman, Abdulhal, Ayman, Abel, Samy, Abergel, Armand, Aberrane, Saïd, Abraham, Bruno, Adler, Maxime, Agard, Christian, Agha-Mir, Ilhem, Aguilar, Claire, Agulles, Baptiste, Aldallal, Hamza, Alric, Laurent, Amiot, Xavier, Andrau, Pierre, Andrieux, Vladimir, Ansart, Séverine, Anty, Rodolphe, Archambeaud, Isabelle, Arem, Samir, Armand, Laurence, Aubailly, Lucie, Audibert, Juliette, Auguereau, Olivier, Auvray, Christelle, Aziz, Karime, Bachelier, Marie-Nadège, Bacquaert-Dufour, Karine, Badet, Françoise, Bahallah, Mohamed-Larbi, Balanant, Hélène, Baraduc, Régine, Bardis, Alexandre, Barraud, Olivier, Barrier, Jocelyn, Baudet, Antoine, Baumert, Thomas, Beaugerie, Laurent, Bébéar, Cécile, Becheur, Hakim, Bemer, Pascale, Benard, Caroline, Benezet, Marie-Pierre, Benmahammed, Mohammed, Bennouna, Jaafar, Benseddik, Zehaira, Bensimon, Pierre-Yves, Bental, Abdeslam, Berete, Aliou, Bergier, Jean-Michel, Berkani, Wacila, Bernardi, Franck, Bert, Frederic, Bertrou, Anne, Beuret, Pascal, Beurton-Chataigner, Isabelle, Beuscart, Claude, Beusnel, Christine, Bevilacqua, Sibylle, Beze, François, Bideau, Karine, Bidegain, Frédéric, Billon, Laura, Blaison, Gilles, Blanc, Michèle, Blanc, Pierre, Blanchi, Sophie, Blancho, Gilles, Bland, Stephane, Blondeau, Vincent, Boldron, Amale, Bon, Djemah, Bonacorsi, Stéphane, Bonzon, Lucas, Borderon, Anaïs, Botelho-Nevers, Elisabeth, Bottlaender, Jacques, Bouc-Boucher, Mathilde, Bouchaud, Olivier, Bougon, David, Boukelikha, Khaled, Bourlet, Thomas, Boussoukaya, Samy, Boutaleb, Hamza, Bouziges, Nicole, Bray, Philippe, Bréchet, Caroline, Bret, Laurent, Brieu, Nathalie, Briffaut, David, Brochet, Christine, Brulez-Des-Varannes, Stanislas, Brunel, Valéry, Brung-Lefebvre, Maud, Bureau, Christophe, Burucoa, Christophe, Buscail, Louis, Buzele, Rodolphe, Cadot, Catherine, Cadranel, Jean-Francois, Cady, Anne, Caillon, Jocelyne, Camiade, Sabine, Campillo, Bernard, Carbonnel, Franck, Carbonnelle, Etienne, Cardot-Martin, Émilie, Cariou, Marie-Estelle, Carles, Michel, Caron, Francois, Carrara-Delarue, Lucrecia, Carrier, Paul, Castang, Céline, Castellano, Inès, Cattoir, Vincent, Caubet, Olivier, Causse, Xavier, Chabrol, Amélie, Chanard, Emmanuel, Chatagnon, Thomas, Chazouilleres, Olivier, Chedanni, Halima, Chevrel, Pauline, Chirol, Catherine, Chirouze, Catherine, Chouquer, Renaud, Clavière, Christophe, Codreuil, Sylvain, Colardelle, Philippe, Combarnous, François, Commeau, Grégory, Cornillet, Anne, Corvec, Stephane, Costa, Yannick, Couderc, Philippe, Couffon, Caroline, Courivaud, Cécile, Courtade, Henri, Cruchant, Etienne, Cuen, David, Culard, Jean-François, Cung, Hong Ahn, Dahyot, Sandrine, D'Altéroche, Louis, Dao, Manh Thông, Darfeuil, Fabien, Darnaud, Céline, Daure, Sophie, De Grossouvre-Taillefer, Ludivine, Debriel, Dominique, Debrueres, Jacques, Decaens, Thomas, Decambron, Audrey, Decre-Grapinet, Dominique, Degand, Nicolas, Dehaye, Bruno, Delacour, Thierry, Delarbe, Jean-Marie, Delobel, Pierre, Delpierre, Éric, Delrez, René, Delvert, Didier, Demartino, Sylvie, Deniel, Marie-Clémence, Denis, Bernard, Derumeaux, Guy, Desroches, Marine, Dessein, Rodrigue, Devillez, Simon, Deweerdt, Didier, Diamantis, Sylvain, Diaz, Emmanuel, Didier, Raffenot, Dimartino, Vincent, Dion, Ludivine, Djemai, Mohand, Doche, Christophe, Donascimento, Maud, Dorval, Ian, Douala, Carol, Doucet-Populaire, Florence, Drouillat, Valérie, Dubée, Vincent, Dudermel, Anne-France, Dumont, Betty, Dupin, Clarisse, Dupont, Mathieu, Dupont, Philippe, Dupuy, Marion, Dupuychaffray, Jean-Pierre, Durand, Francois, Dusser, Pascale, Duval, Valérie, Duveau, Nicolas, El-Azouzi, Abdelghani, El-Gharras, Hynd, Elsendoorn, Antoine, Emile, Loïc, Epaulard, Olivier, Etchepare, Nicolas, Etienne, Jean-Pierre, Eveillard, Mathieu, Evers, Annie, Fach, Joelle, Faizoun, Claudia, Fangous, Marie-Sarah, Farmachidi, Jean Pierre, Fatome, Armelle, Faulques, Bernard, Faure, Karine, Felix, Charlotte, Ferec, Marc, Ferey, Janine, Ferracci, Serge, Feryn, Jean-Marc, Fesler, Pierre, Fiette, Hélène, Flevin, Emilie, Floch, Pauline, Fort, Eric, Fortineau, Nicolas, Fourcade, Jacques, Fraissinet, François, Franck, Patricia, Françoise, Thiebaut, Fratte, Serge, Galempoix, Jean-Marc, Garcera, Yves, Garcia, Anne, Garcon, Pierre, Garret, Charlotte, Gayet, Clement, Gazeau, Pierre, Gerber, Florence, Gilles, Raclot, Gillot, Jean-Michel, Goarant, Eric, Godreuil, Sylvain, Goret, Julien, Gorret, Julie, Goujard, Cecile, Goulenok, Thiphaine, Gournay, Jérôme, Gousseff, Marie, Goux, Alain, Graf, Emmanuelle, Grange, Jean-Didier, Gravet, Alain, Greder-Belan, Alix, Gronier, Olivier, Grosset, Marine, Guellouz, Sabra, Guenenna, Dalida, Guerbaa, Mohammed, Guerin, Meggie, Guerrot, Dominique, Guery, Benoit, Gugenheim, Jean, Guidet, Bertrand, Guiheneuf, Raphael, Guillet-Caruba, Christelle, Guimard, Yves, Guinard, Jérome, Guindre, Laure, Hagege, Albert, Hagege, Hervé, Haineaux, Paul-Arthur, Hamon, Rémy, Hassan, Firas, Hassine, Mélanie, Helie, Ludovic, Herber-Mayne, Anne, Hervio, Pascale, Héry-Arnaud, Geneviève, Hitoto, Hikombo, Hubsch, Théophile, Hunaut, Nicolas, Hurtova, Monika, Husson-Wetzel, Stéphanie, Hutin, Pascal, Izopet, Théo, Jacob, Jean-Louis, Jacomet, Christine, Jaffar-Bandjee, Marie-Christine, Janvier, Fréderic, Jaulhac, Benoît, Jaureguiberry, Stephane, Javaud, Nicolas, Jeannot, Katty, Joundy, Noureddine, Kacem, Moez, Karama, Rouis, Karsenti, David, Kempf, Marie, Khatibi, Sarah, Kikolski, Florence, Kittirath, Christine, Koch, Stephane, Kouatchet-Achille, Tchamba, Krummel, Yves, La Combe, Karine, Labarriere, Damien, Laberenne, Jean-Eric, Lacroix, Hervé, Ladrat, Laure, Lagarde, Stéphanie, Lagasse, Jean-Paul, Laggoune, Ahmed-Saïd, Lambare, Benedicte, Landgraf, Nathalie, Landraud, Luce, Laude, Jean-Francois, Laurent, François, Lavigne, Jean-Philippe, Lavoue, Vincent, Le Berre, Rozenn, Le Goff, Vallérie, Lebars, Hervé, Lebrun, Armandine, Lecapitaine, Anne-Lise, Lechat, Sylvie, Lecoustumier, Alain, Ledreau, Gérard, Lefevre, Benjamin, Leflon, Véronique, Lefort, Agnès, Legall, Florence, Legoff, Isabelle, Legrand, Eric, Lehello, Simon, Le-Henaff-Bourhis, Catherine, Leleu, Olivier, Lelievre, Lucie, Lemaignen, Adrien, Lemaire, Xavier, Le-Maout, Charles, Lemblé, Chantal, Lemeille, Yolande, Lemenand, Olivier, Lemeunier, Violaine, Lemeur, Yannick, Lemierre, Sylvia, Leotard, Sophie, Lepileur, Lucie, Letellier-Demonchy, Claire, Levecq, Hervé, Levy, Marc, Limal, Nicolas, Locher, Christophe, Lopez, Benjamin, Loron, Marie-Charlotte, Loulergue, Joelle, Loury-Larivière, Isabelle, Loustaud-Ratti, Véronique, Macchi, Valèrie, Machado, Moise, Madaule, Serge, Mainardi, Jean-Luc, Males, Silvija, Malherbe, Philippe, Maneglier, Benjamin, Marceau, Maryline, Marcel, Kévin, Marmonier, Alain, Martha, Benoît, Martin, Xavier, Martin-Blondel, Guillaume, Martinez, Camille, Marty, Fabrice, Marty, Patrick, Matray, Olivier, Maurin, Arnaud, Mazerand, Sandie, Mazouz, Nadia, Medevielle, Muriel, Mercat, Alain, Méreghetti, Laurent, Merzoug, Noureddine, Meziane, Ilham, Michaud, Anthony, Michel, Marc, Michel, Pierre, Mignard, Sophie, Milesi-Lecat, Anne-Marie, Mion, Mathieu, Mnasri, Nabil, Mohareb, Abdo, Mohib, Samir, Moindrot, Henri, Monlun, Eric, Montewis, Audrey, Morin, Thierry, Moussata, Driffa, Muller, Sandrine, Muzellec, Valérie, Nancey, Stéphane, Nassereddine, Ahmad, Naude, Sebastien, Neau, Didier, Ovidiu, Negru Calin, Ngo, Thuy, Ngwhotue, Marthe-Andree, Nivet, Patrick, Nordmann, Patrice, Nousbaum, Jean-Baptiste, Nouvel, Bernadette, Obled, Stephane, Oswald, Eric, Otto, Marie-Pierre, Pageaux, Georges-Philippe, Papin, Gregory, Parant, Fabrice, Patenotte, Arnaud, Paupard, Thierry, Pauwels, Arnaud, Pawlotsky, Jean Michel, Pelloux, Hervé, Perlemuter, Gabriel, Peron, Jean-Marie, Pestel-Caron, Martine, Peter, Natasha, Petillon, Sophie, Petit, Richard, Petitprez, Helene, Pettinelli, Francois, Phelip, Jean Marc, Philit, Jean-Baptiste, Phoutthasang, Valérie, Pialoux, Gilles, Piau-Couapel, Caroline, Pichard, Benoit, Pichon, Maxime, Picon-Coste, Magali, Picque, Marie, Pierson, Henri, Piques, Jean Francois, Piton, Béatrice, Planade, Orianne, Plassart, Claire, Plésiat, Patrick, Ploy, Marie-Cécile, Poubeau, Patrice, Pouderoux, Philippe, Pouedras, Pascal, Pourbaix, Annabelle, Poynard, Thierry, Preau, Florence, Pricope, Dumitrita, Queffelec, Gwenaëlle, Queneherve, Lucille, Quentin, Thomas, Raffenot, Didier, Rakotoniaina, Daniella, Ramanantsoa, Celine, Ramarijaona, Solofoniaina, Rami-Arab, Lila, Raulin, Olivia, Rebibou, Jean Michel, Renault, David, Rey, Philippe, Riche, Agnès, Rigaud, Jean Philippe, Rivière, Antoine, Rivière, Brigitte, Robert, Jérôme, Roblot, Pascal, Roger, Helene, Rolland, Christophe, Rondinaud, Emilie, Rosa-Hezode, Isabelle, Roubille, Martine, Rouquette, Olivier, Roux, Juliette, Ruimy, Raymond, Sachot-Ollivier, Sonia, Sailler, Laurent, Salamant, Sarah, Sarbu-Pop, Silvia, Sartre, Jacques, Schmitt, François, Scribe-Outtas, Myriam, Sefrioui, David, Sehouane, Rachid, Sekhri, Hacène, Serfaty, Lawrence, Sevin, Odile, Shawali, Cédric, Siladi, Souad, Silvain, Christine, Simon, Mireille, Simonet, Batiste, Sinayoko, Leila, Sirach, Estelle, Smati, Mustafa, Smets, Aurélie, Soltani, Dhaoui, Sommabere, André, Soulier-Guerin, Karine, Soulillou, Jean Paul, Soupison, Alain, Souply, Laurent, Soussy, Claude-James, Stampfli, Claire, Strullu, Bernard, Suatean, Diana, Tadjerouni, Nacer, Talarmin, Jean-Philippe, Tankovic, Jacques, Tarroun, Abdullah, Tchuenbou, Juliette, Teboul, Jean-Louis, Tedlaouti, Husni, Tellini, Charlotte, Thabut, Dominique, Thannberger, Philippe, Thiebault, Henri, Thiebaut, Françoise, Thomazeau, Joséphine, Tielman, Guillaume, Timsit, Jean-Francois, Tognon, Patrick, Tougeron, David, Toure, Fatouma, Tran, Albert, Tranvouez, Jean-Luc, Trésallet, Christophe, Trubert, Lise, Tsakiris, Laurent, Twizeyimana, Eterne, Vachee, Anne, Valade, Hélène, Valat, Isabelle, Vandendriessche, Anne, Vandermee, Nathalie, Vanheste, Marc, Varon, Emmanuelle, Vasse, Marc, Vasseur, Philippe, Vaucel, Elisabeth, Vauthier, Anne, Verdavaine-Loidreau, Delphine, Verdet, Charlotte, Verdon, Renaud, Vergnaud, Michel, Véziris, Nicolas, Vignaud, Guillaume, Viguier, Jérôme, Villemain, Marc, Villeneuve, Laurent, Vimont-Vicary, Alexandre, Vincent, Thomas, Vuillemenot, Jean-Baptiste, Walewski, Violaine, Warmoes, Elodie, Watry, Hélène, Weber, Jean-Christophe, Witz, Marie Thérèse, Woerther, Paul-Louis, Yazdanpanah, Yazdan, Zamfir, Oana, Zarka, Jonathan, Zavadil, Patrick, Zeboudj, Nabil, Zerbib, Franck, Blanchard, Florian, Henry, Benoît, Vijayaratnam, Sofieya, Canouï, Etienne, Moura, Alexandra, Thouvenot, Pierre, Bracq-Dieye, Hélène, Tessaud-Rita, Nathalie, Valès, Guillaume, Diakité, Andrée, Leclercq, Alexandre, Lecuit, Marc, and Charlier, Caroline

Published
2024
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22. The design of climate-adaptive water subsidies: financial incentives for urban water conservation in Morocco

Author

Zachary Burt, Susan Leal, James Workman, Michael McElroy, and Hynd Bouhia

Subjects
climate adaptation, conservation-oriented pricing, demand management, mena, subsidized water services, utility policy, Environmental technology. Sanitary engineering, TD1-1066
Abstract

In a 500-household pilot, we tested an innovative approach to water demand management, implemented in collaboration with a water utility in a large city in the Middle East and North Africa (MENA) region. We provided a novel intervention, called a Water Savings Credit (WSC), which granted participants volumetric rebates on their water bills for their reductions in water consumption. WSCs were effective at encouraging conservation in our pilot in Marrakech. Our approach has the benefits of a price incentive, without the political risk of a tariff increase. For urban water utilities that provide highly subsidized services, this approach could ultimately pay for itself, or potentially result in net financial savings. Our approach may be especially effective in the countries of the MENA region, as the region has a high rate of subsidization for water services, and because it is facing increasing water scarcity from economic growth, urbanization, and climate change. HIGHLIGHTS A Water Savings Credit (WSC) is a novel intervention that provides a volumetric reward for reduced consumption.; WSCs were effective at encouraging conservation in our pilot in Marrakech.; WSCs have the potential to be more politically acceptable than rate increases and can protect equitable access while encouraging conservation.;

Published
2023
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23. Design and methodology for a proof of mechanism study of individualized neuronavigated continuous Theta burst stimulation for auditory processing in adolescents with autism spectrum disorder

Author

Lindsay M. Oberman, Sunday M. Francis, Lysianne Beynel, Megan Hynd, Miguel Jaime, Pei L. Robins, Zhi-De Deng, Jeff Stout, Jan Willem van der Veen, and Sarah H. Lisanby

Subjects
continuous theta burst stimulation, Autism spectrum disorder, magnetoencephalography, auditory processing, magnetic resonance spectroscopy, magnetic resonance imaging, Psychiatry, RC435-571
Abstract

It has been suggested that aberrant excitation/inhibition (E/I) balance and dysfunctional structure and function of relevant brain networks may underlie the symptoms of autism spectrum disorder (ASD). However, the nomological network linking these constructs to quantifiable measures and mechanistically relating these constructs to behavioral symptoms of ASD is lacking. Herein we describe a within-subject, controlled, proof-of-mechanism study investigating the pathophysiology of auditory/language processing in adolescents with ASD. We utilize neurophysiological and neuroimaging techniques including magnetic resonance spectroscopy (MRS), diffusion-weighted imaging (DWI), functional magnetic resonance imaging (fMRI), and magnetoencephalography (MEG) metrics of language network structure and function. Additionally, we apply a single, individually targeted session of continuous theta burst stimulation (cTBS) as an experimental probe of the impact of perturbation of the system on these neurophysiological and neuroimaging outcomes. MRS, fMRI, and MEG measures are evaluated at baseline and immediately prior to and following cTBS over the posterior superior temporal cortex (pSTC), a region involved in auditory and language processing deficits in ASD. Also, behavioral measures of ASD and language processing and DWI measures of auditory/language network structures are obtained at baseline to characterize the relationship between the neuroimaging and neurophysiological measures and baseline symptom presentation. We hypothesize that local gamma-aminobutyric acid (GABA) and glutamate concentrations (measured with MRS), and structural and functional activity and network connectivity (measured with DWI and fMRI), will significantly predict MEG indices of auditory/language processing and behavioral deficits in ASD. Furthermore, a single session of cTBS over left pSTC is hypothesized to lead to significant, acute changes in local glutamate and GABA concentration, functional activity and network connectivity, and MEG indices of auditory/language processing. We have completed the pilot phase of the study (n=20 Healthy Volunteer adults) and have begun enrollment for the main phase with adolescents with ASD (n=86; age 14-17). If successful, this study will establish a nomological network linking local E/I balance measures to functional and structural connectivity within relevant brain networks, ultimately connecting them to ASD symptoms. Furthermore, this study will inform future therapeutic trials using cTBS to treat the symptoms of ASD.

Published
2024
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24. Two critical times for the SIR model

Author

Hynd, Ryan, Ikpe, Dennis, and Pendleton, Terrance

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Analysis of PDEs
Abstract

We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and infected populations and characterize them as solutions of a certain partial differential equation. This allows us to obtain integral representations of these times and in turn to estimate them precisely for large populations.

Published
2020

25. Continuous time approximation of Nash equilibria

Author

Awi, Romeo, Hynd, Ryan, and Mawi, Henok

Subjects
Mathematics - Analysis of PDEs, Mathematics - Optimization and Control
Abstract

We consider the problem of approximating Nash equilibria of $N$ functions $f_1,\dots, f_N$ of $N$ variables. In particular, we deduce conditions under which systems of the form $$ \dot u_j(t)=-\nabla_{x_j}f_j(u(t)) $$ $(j=1,\dots, N)$ are well posed and in which the large time limits of their solutions $u(t)=(u_1(t),\dots, u_N(t))$ are Nash equilibria for $f_1,\dots, f_N$. To this end, we will invoke the theory of maximal monotone operators. We will also identify an application of these ideas in game theory and show how to approximate equilibria in some game theoretic problems in function spaces.

Published
2020

26. An eradication time problem for the SIR model

Author

Hynd, Ryan, Ikpe, Dennis, and Pendleton, Terrance

Subjects
Mathematics - Analysis of PDEs, Mathematics - Optimization and Control
Abstract

We consider a susceptible, infected, and recovered infectious disease model which incorporates a vaccination rate. In particular, we study the problem of choosing the vaccination rate in order to reduce the number of infected individuals to a given threshold as quickly as possible. This is naturally a problem of time-optimal control. We interpret the optimal time as a solution of two dynamic programming equations and give necessary and sufficient conditions for a vaccination rate to be optimal.

Published
2020

27. Extremals in nonlinear potential theory

Author

Hynd, Ryan and Seuffert, Francis

Subjects
Mathematics - Analysis of PDEs
Abstract

We consider the PDE $-\Delta_pu=\rho$, where $\rho$ is a signed Borel measure on $\mathbb{R}^n$. For each $p>n$, we characterize solutions as extremals of a generalized Morrey inequality determined by $\rho$.

Published
2020

28. On the symmetry and monotonicity of Morrey extremals

Author

Hynd, Ryan and Seuffert, Francis

Subjects
Mathematics - Analysis of PDEs
Abstract

We employ Clarkson's inequality to deduce that each extremal of Morrey's inequality is axially symmetric and is antisymmetric with respect to reflection about a plane orthogonal to its axis of symmetry. We also use symmetrization methods to show that each extremal is monotone in the distance from its axis of symmetry and in the direction of its axis when restricted to spheres centered at the intersection of its axis and its antisymmetry plane.

Published
2019

30. Asymptotic flatness of Morrey extremals

Author

Hynd, Ryan and Seuffert, Francis

Subjects
Mathematics - Analysis of PDEs
Abstract

We study the limiting behavior as $|x|\rightarrow \infty$ of extremal functions $u$ for Morrey's inequality on $\mathbb{R}^n$. In particular, we compute the limit of $u(x)$ as $|x|\rightarrow \infty$ and show $|x||Du(x)|$ tends to $0$. To this end, we exploit the fact that extremals are uniformly bounded and that they each satisfy a PDE of the form $-\Delta_pu=c(\delta_{x_0}-\delta_{y_0})$ for some $c\in \mathbb{R}$ and distinct $x_0,y_0\in \mathbb{R}^n$. More generally, we explain how to quantitatively deduce the asymptotic flatness of bounded $p$-harmonic functions on exterior domains of $\mathbb{R}^n$ for $p>n$.

Published
2019

31. A trajectory map for the pressureless Euler equations

Author

Hynd, Ryan

Subjects
Mathematics - Analysis of PDEs
Abstract

We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide. The equations of motion are a pair of partial differential equations for the particles' mass distribution and local velocity. We show that solutions of this system exist for given initial conditions by rephrasing these equations in Lagrangian coordinates and then by solving for the associated trajectory map.

Published
2019

32. Lagrangian coordinates for the sticky particle system

Author

Hynd, Ryan

Subjects
Mathematics - Analysis of PDEs
Abstract

The sticky particle system is a system of partial differential equations which assert the conservation of mass and momentum of a collection of particles that interact only via inelastic collisions. These equations arise in Zel'dovich's theory for the formation of large scale structures in the universe. We will show that this system of equations has a solution in one spatial dimension for given initial conditions by generating a trajectory mapping in Lagrangian coordinates.

Published
2019

34. Newton's second law with a semiconvex potential

Author

Hynd, Ryan

Subjects
Mathematics - Analysis of PDEs
Abstract

We make the elementary observation that the differential equation associated with Newton's second law $m\ddot\gamma(t)=-D V(\gamma(t))$ always has a solution for given initial conditions provided that the potential energy $V$ is semiconvex. That is, if $-D V$ satisfies a one-sided Lipschitz condition. We will then build upon this idea to verify the existence of solutions for the Jeans-Vlasov equation, the pressureless Euler equations in one spatial dimension and the equations of elastodynamics under appropriate semiconvexity assumptions.

Published
2018

35. Lipschitz regularity for a homogeneous doubly nonlinear PDE

Author

Hynd, Ryan and Lindgren, Erik

Subjects
Mathematics - Analysis of PDEs
Abstract

We study the doubly nonlinear PDE $$ |\partial_t u|^{p-2}\,\partial_t u-\textrm{div}(|\nabla u|^{p-2}\nabla u)=0. $$ This equation arises in the study of extremals of Poincar\'e inequalities in Sobolev spaces. We prove spatial Lipschitz continuity and H\"older continuity in time of order $(p-1)/p$ for viscosity solutions. As an application of our estimates, we obtain pointwise control of the large time behavior of solutions.

Published
2018

36. Perimenopausal Effects of Estradiol on Anhedonia and Psychosis Study (PEEPs): study protocol for a neural and molecular mechanistic clinical trial

Author

Melissa J. M. Walsh, Kathryn Gibson, Megan Hynd, Tory A. Eisenlohr-Moul, Erin C. Walsh, Lauren Schiff, Fred Jarskog, David Lalush, Gabriel S. Dichter, and Crystal E. Schiller

Subjects
Menopause, Depression, Anhedonia, Psychosis, Estrogen, Rewards, Medicine (General), R5-920
Abstract

Abstract Background The perimenopausal transition is accompanied by psychiatric symptoms in over 10% of women. Symptoms commonly include depressed mood and anhedonia and less commonly include psychosis. Psychiatric symptoms have been linked to the depletion and/or variability of circulating estradiol, and estradiol treatment reduces perimenopausal anhedonia and psychosis in some women. Estrogen fluctuations may disrupt function in the mesolimbic reward system in some women, leading to psychiatric symptoms like anhedonia or psychosis. The Perimenopausal Effects of Estradiol on Anhedonia and Psychosis Study (PEEPs) is a mechanistic clinical trial that aims to (1) identify relationships between perimenopausal-onset anhedonia and psychosis and neuromolecular markers of mesolimbic reward responses and (2) determine the extent to which estradiol treatment-induced changes in mesolimbic reward responses are associated with alleviation of perimenopausal onset anhedonia or psychosis. Methods This study will recruit 100 unmedicated women ages 44–55 in the late-stage perimenopausal transition, sampling across the range of mild-to-high anhedonia and absent-to-moderate psychosis symptoms. Patients will be randomized to receive either estradiol or placebo treatment for 3 weeks. Clinical outcome measures will include symptoms of anhedonia (measured with Snaith–Hamilton Pleasure Scale; SHAPS) and psychosis (measured with Brief Psychiatric Rating Scale; BPRS psychosis subscale) as well as neural markers of mesolimbic reward system functioning, including reward-related fMRI activation and PET-derived measure of striatal dopamine binding. Pre-treatment associations between (1) SHAPS/BPRS scores and (2) reward-related striatal dopamine binding/BOLD activation will be examined. Furthermore, longitudinal mixed models will be used to estimate (1) symptom and neuromolecular trajectories as a function of estradiol vs. placebo treatment and (2) how changes in reward-related striatal dopamine binding and BOLD activation predict variability in symptom trajectories in response to estradiol treatment. Discussion This clinical trial will be the first to characterize neural and molecular mechanisms by which estradiol treatment ameliorates anhedonia and psychosis symptoms during the perimenopausal transition, thus laying the groundwork for future biomarker research to predict susceptibility and prognosis and develop targeted treatments for perimenopausal psychiatric symptoms. Furthermore, in alignment with the National Institute for Mental Health Research Domain Criteria initiative, this trial will improve our understanding of a range of disorders characterized by anhedonia, psychosis, and reward system dysfunction. Trial registration ClinicalTrials.gov NCT05282277

Published
2023
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37. Book Reviews

Author

Hynd, Alexander M. and Edge, Lonnie

Published
2022

41. Synthesis of Metallic Nanostructures Using Ionizing Radiation and Their Applications

Author

Hynd Remita and Isabelle Lampre

Subjects
ionizing radiation, radiolysis, metallic nanoparticles, nucleation, redox properties, optical properties, Technology, Electrical engineering. Electronics. Nuclear engineering, TK1-9971, Engineering (General). Civil engineering (General), TA1-2040, Microscopy, QH201-278.5, Descriptive and experimental mechanics, QC120-168.85
Abstract

This paper reviews the radiation-induced synthesis of metallic nanostructures and their applications. Radiolysis is a powerful method for synthesizing metallic nanoparticles in solution and heterogeneous media, and it is a clean alternative to other existing physical, chemical, and physicochemical methods. By varying parameters such as the absorbed dose, dose rate, concentrations of metallic precursors, and nature of stabilizing agents, it is possible to control the size, shape, and morphology (alloy, core-shell, etc.) of the nanostructures and, consequently, their properties. Therefore, the as-synthesized nanoparticles have many potential applications in biology, medicine, (photo)catalysis, or energy conversion.

Published
2024
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43. Extremal functions for Morrey's inequality

Author

Hynd, Ryan and Seuffert, Francis

Subjects
Mathematics - Analysis of PDEs
Abstract

We give a qualitative description of extremals for Morrey's inequality. Our theory is based on exploiting the invariances of this inequality, studying the equation satisfied by extremals and the observation that extremals are optimal for a related convex minimization problem.

Published
2018

44. Sticky particles and the pressureless Euler equations in one spatial dimension

Author

Hynd, Ryan

Subjects
Mathematics - Analysis of PDEs
Abstract

We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they remain stuck together thereafter. Our main result is that if the interaction potential is semi-convex, this sticky particle property can quantified and is preserved upon letting the number of particles tend to infinity. This is used to show that solutions of the pressureless Euler equations exist for given initial conditions and satisfy an entropy inequality.

Published
2018

45. Probability measures on the path space and the sticky particle system

Author

Hynd, Ryan

Subjects
Mathematics - Analysis of PDEs
Abstract

We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles stick together and explain how to associate a probability measure on the space of continuous paths to such a collection of evolving point masses. These observations lead to a new method of designing solutions to the sticky particle system in one spatial dimension which have nonincreasing kinetic energy and satisfy an entropy inequality.

Published
2018

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