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## Decisions in Economics and Finance

### A Journal of Applied Mathematics

 Short Title: Decis. Econ. Finance Publisher: Springer, Milan ISSN: 1593-8883; 1129-6569/e Online: http://link.springer.com/journal/volumesAndIssues/10203 Predecessor: Rivista di Matematica per le Scienze Economiche e Sociali Comments: Indexed cover-to-cover
 Documents Indexed: 362 Publications (since 2000) References Indexed: 322 Publications with 8,944 References.
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### Latest Issues

 45, No. 1 (2022) 44, No. 2 (2021) 44, No. 1 (2021) 43, No. 2 (2020) 43, No. 1 (2020) 42, No. 2 (2019) 42, No. 1 (2019) 41, No. 2 (2018) 41, No. 1 (2018) 40, No. 1-2 (2017) 39, No. 2 (2016) 39, No. 1 (2016) 38, No. 2 (2015) 38, No. 1 (2015) 37, No. 2 (2014) 37, No. 1 (2014) 36, No. 2 (2013) 36, No. 1 (2013) 35, No. 2 (2012) 35, No. 1 (2012) 34, No. 2 (2011) 34, No. 1 (2011) 33, No. 2 (2010) 33, No. 1 (2010) 32, No. 2 (2009) 32, No. 1 (2009) 31, No. 2 (2008) 31, No. 1 (2008) 30, No. 2 (2007) 30, No. 1 (2007) 29, No. 2 (2006) 29, No. 1 (2006) 28, No. 2 (2005) 28, No. 1 (2005) 27, No. 2 (2004) 27, No. 1 (2004) 26, No. 2 (2003) 26, No. 1 (2003) 25, No. 2 (2002) 25, No. 1 (2002) 24, No. 2 (2001) 24, No. 1 (2001) 23, No. 2 (2000) 23, No. 1 (2000)
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### Authors

 6 Sodini, Mauro 6 Tramontana, Fabio 5 Naimzada, Ahmad K. 5 Radi, Davide 5 Szidarovszky, Ferenc P. 4 Carosi, Laura 4 Costabile, Massimo 4 Figà-Talamanca, Gianna 4 Gardini, Laura 4 Grasselli, Martino 4 Herzel, Stefano 4 Korn, Ralf 4 Kwok, Yue-Kuen 4 Leung, Chi Man 4 Mancino, Maria Elvira 4 Matsumoto, Akio 4 Pressacco, Flavio 4 Vargiolu, Tiziano 4 Wong, Kit Pong 4 Zanette, Antonino 3 Alòs, Elisa 3 Antonelli, Fabio 3 Bernard, Carole L. 3 Cerboni Baiardi, Lorenzo 3 Dal Forno, Arianna 3 De Angelis, Paolo 3 Ferrara, Massimiliano 3 Gori, Luca 3 Guerrini, Luca 3 Kountzakis, Christos E. 3 Lamantia, Fabio 3 Menegatti, Mario 3 Michetti, Elisabetta 3 Patacca, Marco 3 Sabino, Piergiacomo 3 Westerhoff, Frank H. 2 Alcantud, José Carlos Rodríguez 2 Amarante, Massimiliano 2 Andrikopoulos, Athanasios 2 Angelini, Flavio 2 Assa, Hirbod 2 Biancardi, Marta Elena 2 Bisceglia, Michele 2 Blot, Joël 2 Broll, Udo 2 Brunelli, Matteo 2 Cambini, Riccardo 2 Campisi, Giovanni 2 Caravaggio, Andrea 2 Cassese, Gianluca 2 Cavalli, Fausto 2 Cavallo, Bice 2 Corazza, Marco 2 Cretarola, Alessandra 2 Crettez, Bertrand 2 D’Amico, Guglielmo 2 De Donno, Marzia 2 De Gennaro Aquino, Luca 2 De Marchis, Roberto 2 D’Ecclesia, Rita Laura 2 Dieci, Roberto 2 Ewald, Christian-Oliver 2 Fajardo, José 2 Fanti, Luciano 2 Fedrizzi, Michele 2 Galeotti, Marcello 2 Gaudenzi, Marcellino 2 Gori, Michele 2 Grassetti, Francesca 2 Graziano, Maria Gabriella 2 Grilli, Luca 2 Hobson, David Graham 2 Jeanblanc, Monique 2 Kopel, Michael 2 le Courtois, Olivier 2 Leccadito, Arturo 2 Levantesi, Susanna 2 Maddalena, Lucia 2 Mammana, Cristiana 2 Manca, Raimondo 2 Mari, Carlo 2 Marinacci, Massimo 2 Martire, Antonio Luciano 2 Mastroeni, Loretta 2 Merlone, Ugo 2 Modica, Salvatore 2 Montrucchio, Luigi 2 Nardon, Martina 2 Pansera, Bruno Antonio 2 Pianca, Paolo 2 Pireddu, Marina 2 Quittard-Pinon, François M. 2 Rásonyi, Miklós 2 Rigo, Pietro 2 Rossello, Damiano 2 Ryan, Matthew J. 2 Sanfelici, Simona 2 Sass, Jörn 2 Schäl, Manfred 2 Sibillo, Marilena ...and 489 more Authors
all top 5

### Fields

 346 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 69 Probability theory and stochastic processes (60-XX) 43 Statistics (62-XX) 31 Operations research, mathematical programming (90-XX) 19 Systems theory; control (93-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 12 Dynamical systems and ergodic theory (37-XX) 12 Numerical analysis (65-XX) 10 General and overarching topics; collections (00-XX) 10 Computer science (68-XX) 6 Ordinary differential equations (34-XX) 6 Partial differential equations (35-XX) 4 History and biography (01-XX) 4 Functional analysis (46-XX) 3 Measure and integration (28-XX) 3 Approximations and expansions (41-XX) 2 Combinatorics (05-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Convex and discrete geometry (52-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 General topology (54-XX)

### Citations contained in zbMATH Open

183 Publications have been cited 774 times in 725 Documents Cited by Year
Knightian decision theory. I. Zbl 1041.91023
Bewley, Truman F.
2002
Decision analysis using targets instead of utility functions. Zbl 1051.91503
Bordley, Robert; LiCalzi, Marco
2000
Homogeneous semi-Markov reliability models for credit risk management. Zbl 1125.91341
D’Amico, Guglielmo; Janssen, Jacques; Manca, Raimondo
2005
Optimal consumption and investment under partial information. Zbl 1165.91410
Putschögl, Wolfgang; Sass, Jörn
2008
Conditional comonotonicity. Zbl 1063.60002
Jouini, Elyès; Napp, Clotilde
2004
Option pricing by large risk aversion utility under transaction costs. Zbl 1011.91043
Bouchard, B.; Kabanov, Yu. A.; Touzi, N.
2001
Financial economics without probabilistic prior assumptions. Zbl 1398.91613
Riedel, Frank
2015
The Aubin private core of differential information economies. Zbl 1125.91383
Graziano, Maria Gabriella; Meo, Claudia
2005
A bidimensional approach to mortality risk. Zbl 1160.91366
Biffis, Enrico; Millossovich, Pietro
2006
Normal approximations by Stein’s method. Zbl 0985.60024
Rinott, Yosef; Rotar, Vladimir
2000
Efficient Monte Carlo pricing of European options using mean value control variates. Zbl 1010.91051
Pellizzari, P.
2001
Optimal impulse control for cash management with quadratic holding-penalty costs. Zbl 1016.93071
Baccarin, Stefano
2002
An efficient binomial method for pricing American options. Zbl 1040.91047
Gaudenzi, Marcellino; Pressacco, Flavio
2003
Pricing VIX options with stochastic volatility and random jumps. Zbl 1273.91442
Lian, Guang-Hua; Zhu, Song-Ping
2013
Discrete-time delay dynamics of boundedly rational monopoly. Zbl 1302.91135
Matsumoto, Akio; Szidarovszky, Ferenc
2014
A combinatorial approach for pricing Parisian options. Zbl 1156.91364
Costabile, Massimo
2002
Path dependent volatility. Zbl 1160.35457
Foschi, Paolo; Pascucci, Andrea
2008
On the smoothness of optimal paths. Zbl 1091.91053
Blot, Joël; Crettez, Bertrand
2004
One-dimensional maps with two discontinuity points and three linear branches: mathematical lessons for understanding the dynamics of financial markets. Zbl 1302.91199
Tramontana, Fabio; Westerhoff, Frank; Gardini, Laura
2014
Markovian lifts of positive semidefinite affine Volterra-type processes. Zbl 1432.91110
Cuchiero, Christa; Teichmann, Josef
2019
Moment explosions in the rough Heston model. Zbl 1432.91123
Gerhold, Stefan; Gerstenecker, Christoph; Pinter, Arpad
2019
Arbitrage, linear programming and martingales in securities markets with bid-ask spreads. Zbl 1137.91468
Ortu, Fulvio
2001
A note on mixture sets in decision theory. Zbl 1019.91013
Mongin, Philippe
2001
The optimal capital structure of the firm with stable Lévy assets returns. Zbl 1160.91014
Le Courtois, Olivier; Quittard-Pinon, François
2008
The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process. Zbl 1137.91455
Korn, Ralf; Oertel, Frank; Schäl, Manfred
2003
Portfolio optimization in a defaultable market under incomplete information. Zbl 1257.91039
Callegaro, Giorgia; Jeanblanc, Monique; Runggaldier, Wolfgang J.
2012
The completion of security markets. Zbl 1152.91525
Kountzakis, Christos; Polyrakis, Ioannis A.
2006
Does market attention affect bitcoin returns and volatility? Zbl 1431.62474
Figá-Talamanca, Gianna; Patacca, Marco
2019
A uniqueness theorem for convex-ranged probabilities. Zbl 0987.28002
Marinacci, Massimo
2000
Reaching nirvana with a defaultable asset? Zbl 1398.91502
Battauz, Anna; De Donno, Marzia; Sbuelz, Alessandro
2017
A migration equilibrium model with uncertain data and movement costs. Zbl 1398.91474
Causa, A.; Jadamba, B.; Raciti, F.
2017
Explicit solutions for shortfall risk minimization in multinomial models. Zbl 1049.91084
Scagnellato, Caterina; Vargiolu, Tiziano
2002
Utility indifference valuation for jump risky assets. Zbl 1273.91192
Ceci, Claudia; Gerardi, Anna
2011
An optimal insurance design problem under Knightian uncertainty. Zbl 1277.91075
Bernard, Carole; Ji, Shaolin; Tian, Weidong
2013
On the construction of optimal payoffs. Zbl 1444.91201
Rüschendorf, L.; Vanduffel, Steven
2020
Volatility estimation from observed option prices. Zbl 0988.91034
Boyle, Phelim P.; Thangaraj, Draviam
2000
Necessary conditions for nonsmooth multiobjective semi-infinite problems using Michel-penot subdifferential. Zbl 1397.90382
Caristi, Giuseppe; Ferrara, Massimiliano
2017
Competition and cooperation in the exploitation of the groundwater resource. Zbl 1419.91544
Biancardi, Marta; Maddalena, Lucia
2018
Bounds for the utility-indifference prices of non-traded assets in incomplete markets. Zbl 1125.91346
Hobson, D. G.
2005
Characterisation of optimal dual measures via distortion. Zbl 1131.60063
Monoyios, Michael
2006
Galerkin infinite element approximation for pricing barrier options and options with discontinuous payoff. Zbl 1106.91035
Sanfelici, Simona
2004
Linear cumulative prospect theory with applications to portfolio selection and insurance demand. Zbl 1218.91038
Schmidt, Ulrich; Zank, Horst
2007
Market attention and Bitcoin price modeling: theory, estimation and option pricing. Zbl 1444.91208
Cretarola, Alessandra; Figà-Talamanca, Gianna; Patacca, Marco
2020
Representing complete and incomplete subjective linear preferences on random numbers. Zbl 1064.91031
Girotto, Bruno; Holzer, Silvano
2003
Pricing American barrier options with discrete dividends by binomial trees. Zbl 1176.91153
Gaudenzi, Marcellino; Zanette, Antonino
2009
Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model. Zbl 1198.91073
Wang, Wen-Kai; Ewald, Christian-Oliver
2010
Sensitivities for Bermudan options by regression methods. Zbl 1198.91202
Belomestny, Denis; Milstein, G. N.; Schoenmakers, John
2010
Genetic algorithm versus classical methods in sparse index tracking. Zbl 1398.91518
Giuzio, Margherita
2017
Risk aversion and risk vulnerability in the continuous and discrete case. Zbl 1257.91021
Bohner, Martin; Gelles, Gregory M.
2012
Hedging and the competitive firm under correlated price and background risk. Zbl 1398.91664
Wong, Kit Pong
2014
Existence of financial equilibria with endogenous short selling restrictions and real assets. Zbl 1398.91390
Gori, Michele; Pireddu, Marina; Villanacci, Antonio
2014
Risk management under a prudential policy. Zbl 1398.91677
Assa, Hirbod
2015
Some reflections on past and future of nonlinear dynamics in economics and finance. Zbl 1419.91475
Anufriev, Mikhail; Radi, Davide; Tramontana, Fabio
2018
Fast and accurate calculation of American option prices. Zbl 1419.91644
Ballestra, Luca Vincenzo
2018
Efficient quasi-Monte simulations for pricing high-dimensional path-dependent options. Zbl 1165.91411
Sabino, Piergiacomo
2009
On the relationship between absolute prudence and absolute risk aversion. Zbl 1160.91331
Maggi, Mario A.; Magnani, Umberto; Menegatti, Mario
2006
Arbitrage and completeness in financial markets with given $$N$$-dimensional distributions. Zbl 1091.91032
Campi, Luciano
2004
Arbitrage pricing theory and risk-neutral measures. Zbl 1106.91029
Rásonyi, Miklós
2004
An algorithm for winning coalitions in indirect control of corporations. Zbl 1010.91005
Prati, Nando; Denti, Enrico
2001
A closed-form solution for the continuous-time consumption model with endogenous labor income. Zbl 1198.91200
Zhang, Aihua
2010
Approximating exact expected utility via portfolio efficient frontiers. Zbl 1398.91509
Carleo, Alessandra; Cesarone, Francesco; Gheno, Andrea; Ricci, Jacopo Maria
2017
Homothetic preferences on star-shaped sets. Zbl 1051.91015
Maccheroni, Fabio
2001
An elementary core equivalence theorem in a countable economy. Zbl 1034.91053
Tasnádi, Attila
2002
How should a convertible bond be decomposed? Zbl 1257.91048
Zhu, Song-Ping; Zhang, Jing
2012
Production and hedging in futures markets with multiple delivery specifications. Zbl 1398.91665
Wong, Kit Pong
2014
Gambling in contests modelled with diffusions. Zbl 1398.91295
Feng, Han; Hobson, David
2015
Oligopoly models with different learning and production time scales. Zbl 1419.91462
2018
Market consistent valuations with financial imperfection. Zbl 1391.91167
Assa, Hirbod; Gospodinov, Nikolay
2018
Taxes and money in incomplete financial markets. Zbl 1151.91661
del Mercato, Elena L.; Villanacci, Antonio
2006
Stochastic demand correspondences and their aggregation properties. Zbl 1151.91397
Alcantud, José C. R.
2006
Stochastic Jacobian and Riccati ODE in affine term structure models. Zbl 1154.60056
Grasselli, Martino; Tebaldi, Claudio
2007
On the smoothness of optimal paths. II. Some local turnpike results. Zbl 1141.91035
Blot, Joël; Crettez, Bertrand
2007
Unawareness, priors and posteriors. Zbl 1165.91350
Modica, Salvatore
2008
A two-step simulation procedure to analyze the exercise features of American options. Zbl 1091.91031
Basso, Antonella; Nardon, Martina; Pianca, Paolo
2004
Continuous-time mean-variance portfolio optimization in a jump-diffusion market. Zbl 1232.91603
Alp, Özge Sezgin; Korn, Ralf
2011
The firm under uncertainty: real and financial decisions. Zbl 1274.91464
Broll, Udo; Wong, Kit Pong
2013
Optimal reinsurance and investment in a diffusion model. Zbl 1444.91191
Brachetta, Matteo; Schmidli, Hanspeter
2020
Semi-analytical prices for lookback and barrier options under the Heston model. Zbl 1432.91121
De Gennaro Aquino, Luca; Bernard, Carole
2019
Option pricing with stochastic volatility models. Zbl 1052.91045
Herzel, Stefano
2000
Groundwater extraction among overlapping generations: a differential game approach. Zbl 1465.91070
Biancardi, Marta; Maddalena, Lucia; Villani, Giovanni
2020
Some new characterization of rational expectation equilibria in economies with asymmetric information. Zbl 1202.91167
De Simone, Anna; Tarantino, Ciro
2010
Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities. Zbl 1398.91399
Bigi, Giancarlo; Passacantando, Mauro
2017
Robust games: theory and application to a Cournot duopoly model. Zbl 1398.91022
Crespi, Giovanni Paolo; Radi, Davide; Rocca, Matteo
2017
Cyclically monotone equilibrium problems and Ekeland’s principle. Zbl 1394.58006
Giuli, Massimiliano
2017
A set optimization approach to utility maximization under transaction costs. Zbl 1398.91258
Hamel, Andreas H.; Wang, Sophie Qingzhen
2017
A differential game in a duopoly with instantaneous incentives. Zbl 1398.91088
Grilli, Luca; Bisceglia, Michele
2017
Optimality in a financial economy with outside money and restricted participation. Zbl 1056.91040
Carosi, Laura
2001
Mean-variance hedging for interest rate models with stochastic volatility. Zbl 1042.91035
Biagini, Francesca
2002
Bargaining over an uncertain outcome: The role of beliefs. Zbl 1042.91002
Billot, Antoine; Chateauneuf, Alain; Gilboa, Itzhak; Tallon, Jean-Marc
2002
Numeraire portfolios and utility-based price systems under proportional transaction costs. Zbl 1398.91545
Sass, Jörn; Schäl, Manfred
2014
An application of nonparametric volatility estimators to option pricing. Zbl 1398.91602
Kenmoe, Romuald N.; Sanfelici, Simona
2014
Using value-at-risk to reconcile limited liability and the moral-hazard problem. Zbl 1398.91659
Tulli, Vanda; Weinrich, Gerd
2015
Diversification preferences in the theory of choice. Zbl 1398.91173
De Giorgi, Enrico G.; Mahmoud, Ola
2016
Real options game models of R&D competition between asymmetric firms with spillovers. Zbl 1398.91655
Leung, Chi Man; Kwok, Yue Kuen
2016
The link between the Shapley value and the beta factor. Zbl 1398.91043
Ortmann, Karl Michael
2016
A note on portfolio selection and stochastic dominance. Zbl 1398.91539
Menegatti, Mario
2016
Optimal portfolio selection via conditional convex risk measures on $$L ^{p }$$. Zbl 1268.91160
Acciaio, Beatrice; Goldammer, Verena
2013
Optimal strategy for a fund manager with option compensation. Zbl 1391.91150
Nicolosi, Marco
2018
Measures of risk attitude: correspondences between mean-variance and expected-utility approaches. Zbl 1136.91384
Eichner, Thomas; Wagener, Andreas
2005
An overlapping generations model with non-ordered preferences and numeraire-incomplete markets. Zbl 1136.91513
Seghir, Abdelkrim
2005
Long versus short time scales: the rough dilemma and beyond. Zbl 1492.91355
Garcin, Matthieu; Grasselli, Martino
2022
Ramsey rule with forward/backward utility for long-term yield curves modeling. Zbl 1492.91395
El Karoui, Nicole; Hillairet, Caroline; Mrad, Mohamed
2022
Challenges in approximating the Black and Scholes call formula with hyperbolic tangents. Zbl 1470.91285
Mininni, Michele; Orlando, Giuseppe; Taglialatela, Giovanni
2021
Breaking ties in collective decision-making. Zbl 07380465
Bubboloni, Daniela; Gori, Michele
2021
Correlating Lévy processes with self-decomposability: applications to energy markets. Zbl 1480.91288
Gardini, Matteo; Sabino, Piergiacomo; Sasso, Emanuela
2021
Longevity risk and economic growth in sub-populations: evidence from Italy. Zbl 1467.91117
Bozzo, Giuseppina; Levantesi, Susanna; Menzietti, Massimiliano
2021
Asian options with zero cost-of-carry: EEX options on freight and iron ore futures. Zbl 1467.91186
Haug, Espen Gaarder
2021
On the construction of optimal payoffs. Zbl 1444.91201
Rüschendorf, L.; Vanduffel, Steven
2020
Market attention and Bitcoin price modeling: theory, estimation and option pricing. Zbl 1444.91208
Cretarola, Alessandra; Figà-Talamanca, Gianna; Patacca, Marco
2020
Optimal reinsurance and investment in a diffusion model. Zbl 1444.91191
Brachetta, Matteo; Schmidli, Hanspeter
2020
Groundwater extraction among overlapping generations: a differential game approach. Zbl 1465.91070
Biancardi, Marta; Maddalena, Lucia; Villani, Giovanni
2020
A special issue on the mathematics of subjective probability. Zbl 1493.00019
2020
A notion of conditional probability and some of its consequences. Zbl 1455.60006
Berti, Patrizia; Dreassi, Emanuela; Rigo, Pietro
2020
Predictive distributions that mimic frequencies over a restricted subdomain. Zbl 1444.62032
Lad, Frank; Sanfilippo, Giuseppe
2020
Changes in multiplicative risks and optimal portfolio choice: new interpretations and results. Zbl 1444.91197
De Donno, Marzia; Magnani, Marco; Menegatti, Mario
2020
Robust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry. Zbl 1465.91124
Mensah, Emmanuel Kwasi
2020
Pricing electricity forwards under future information on the stochastic mean-reversion level. Zbl 1465.91115
Hess, Markus
2020
Markovian lifts of positive semidefinite affine Volterra-type processes. Zbl 1432.91110
Cuchiero, Christa; Teichmann, Josef
2019
Moment explosions in the rough Heston model. Zbl 1432.91123
Gerhold, Stefan; Gerstenecker, Christoph; Pinter, Arpad
2019
Does market attention affect bitcoin returns and volatility? Zbl 1431.62474
Figá-Talamanca, Gianna; Patacca, Marco
2019
Semi-analytical prices for lookback and barrier options under the Heston model. Zbl 1432.91121
De Gennaro Aquino, Luca; Bernard, Carole
2019
Kyle equilibrium under random price pressure. Zbl 1426.91315
Corcuera, José Manuel; Di Nunno, Giulia; Fajardo, José
2019
Volatility and volatility-linked derivatives: estimation, modeling, and pricing. Zbl 1431.91388
Alòs, Elisa; Mancino, Maria Elvira; Wang, Tai-Ho
2019
Robust calibration and arbitrage-free interpolation of SSVI slices. Zbl 1431.91390
Corbetta, Jacopo; Cohort, Pierre; Laachir, Ismail; Martini, Claude
2019
Foreword special issue Deaf 2019 – MAF 2018. Zbl 1481.00042
2019
Small sample properties of ML estimator in Vasicek and CIR models: a simulation experiment. Zbl 1426.91282
Albano, Giuseppina; La Rocca, Michele; Perna, Cira
2019
Variable annuities with a threshold fee: valuation, numerical implementation and comparative static analysis. Zbl 1426.91203
Bacinello, Anna Rita; Zoccolan, Ivan
2019
Lévy CARMA models for shocks in mortality. Zbl 1426.91222
Hitaj, Asmerilda; Mercuri, Lorenzo; Rroji, Edit
2019
Estimation of volatility in a high-frequency setting: a short review. Zbl 1432.91111
Jacod, Jean
2019
From volatility smiles to the volatility of volatility. Zbl 1432.91122
Dumas, Bernard; Luciano, Elisa
2019
Asymptotic expansion for some local volatility models arising in finance. Zbl 1432.91107
Albeverio, Sergio; Cordoni, Francesco; Di Persio, Luca; Pellegrini, Gregorio
2019
A realized volatility approach to option pricing with continuous and jump variance components. Zbl 1432.91117
Alitab, Dario; Bormetti, Giacomo; Corsi, Fulvio; Majewski, Adam A.
2019
Competition and cooperation in the exploitation of the groundwater resource. Zbl 1419.91544
Biancardi, Marta; Maddalena, Lucia
2018
Some reflections on past and future of nonlinear dynamics in economics and finance. Zbl 1419.91475
Anufriev, Mikhail; Radi, Davide; Tramontana, Fabio
2018
Fast and accurate calculation of American option prices. Zbl 1419.91644
Ballestra, Luca Vincenzo
2018
Oligopoly models with different learning and production time scales. Zbl 1419.91462
2018
Market consistent valuations with financial imperfection. Zbl 1391.91167
Assa, Hirbod; Gospodinov, Nikolay
2018
Optimal strategy for a fund manager with option compensation. Zbl 1391.91150
Nicolosi, Marco
2018
A piecewise linear model of credit traps and credit cycles: a complete characterization. Zbl 1419.91634
Matsuyama, Kiminori; Sushko, Iryna; Gardini, Laura
2018
Global indeterminacy and equilibrium selection in a model with depletion of non-renewable resources. Zbl 1419.91543
Bella, Giovanni; Mattana, Paolo
2018
Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity. Zbl 1419.91298
Guerrini, Luca; Pecora, Nicolò; Sodini, Mauro
2018
Technology choice in an evolutionary oligopoly game. Zbl 1419.91468
Lamantia, Fabio; Negriu, Anghel; Tuinstra, Jan
2018
Steady states, stability and bifurcations in multi-asset market models. Zbl 1419.91660
Dieci, Roberto; Schmitt, Noemi; Westerhoff, Frank
2018
Real options signaling game models for dynamic acquisition under information asymmetry. Zbl 1391.91160
Leung, Chi Man; Kwok, Yue Kuen
2018
Reaching nirvana with a defaultable asset? Zbl 1398.91502
Battauz, Anna; De Donno, Marzia; Sbuelz, Alessandro
2017
A migration equilibrium model with uncertain data and movement costs. Zbl 1398.91474
Causa, A.; Jadamba, B.; Raciti, F.
2017
Necessary conditions for nonsmooth multiobjective semi-infinite problems using Michel-penot subdifferential. Zbl 1397.90382
Caristi, Giuseppe; Ferrara, Massimiliano
2017
Genetic algorithm versus classical methods in sparse index tracking. Zbl 1398.91518
Giuzio, Margherita
2017
Approximating exact expected utility via portfolio efficient frontiers. Zbl 1398.91509
Carleo, Alessandra; Cesarone, Francesco; Gheno, Andrea; Ricci, Jacopo Maria
2017
Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities. Zbl 1398.91399
Bigi, Giancarlo; Passacantando, Mauro
2017
Robust games: theory and application to a Cournot duopoly model. Zbl 1398.91022
Crespi, Giovanni Paolo; Radi, Davide; Rocca, Matteo
2017
Cyclically monotone equilibrium problems and Ekeland’s principle. Zbl 1394.58006
Giuli, Massimiliano
2017
A set optimization approach to utility maximization under transaction costs. Zbl 1398.91258
Hamel, Andreas H.; Wang, Sophie Qingzhen
2017
A differential game in a duopoly with instantaneous incentives. Zbl 1398.91088
Grilli, Luca; Bisceglia, Michele
2017
Convex and convex-like optimization over a range inclusion problem and first applications. Zbl 1398.49030
Mokhtar-Kharroubi, Hocine
2017
An axiomatization of continuous quasilinear utility. Zbl 1398.91264
Rébillé, Yann
2017
Weighted average price in the Heston stochastic volatility model. Zbl 1398.91611
Papi, M.; Pontecorvi, L.; Donatucci, C.
2017
Diversification preferences in the theory of choice. Zbl 1398.91173
De Giorgi, Enrico G.; Mahmoud, Ola
2016
Real options game models of R&D competition between asymmetric firms with spillovers. Zbl 1398.91655
Leung, Chi Man; Kwok, Yue Kuen
2016
The link between the Shapley value and the beta factor. Zbl 1398.91043
Ortmann, Karl Michael
2016
A note on portfolio selection and stochastic dominance. Zbl 1398.91539
Menegatti, Mario
2016
The pricing of lookback options and binomial approximation. Zbl 1398.91596
Grosse-Erdmann, Karl; Heuwelyckx, Fabien
2016
On the choice between two delta-hedging strategies. Zbl 1398.91331
Hong, Liang
2016
A representation of risk measures. Zbl 1398.91306
Amarante, Massimiliano
2016
Consumption optimization for recursive utility in a jump-diffusion model. Zbl 1398.91269
Antonelli, Fabio; Mancini, Carlo
2016
Financial economics without probabilistic prior assumptions. Zbl 1398.91613
Riedel, Frank
2015
Risk management under a prudential policy. Zbl 1398.91677
Assa, Hirbod
2015
Gambling in contests modelled with diffusions. Zbl 1398.91295
Feng, Han; Hobson, David
2015
Using value-at-risk to reconcile limited liability and the moral-hazard problem. Zbl 1398.91659
Tulli, Vanda; Weinrich, Gerd
2015
On a fuzzy cash flow model with insurance applications. Zbl 1398.91356
Ungureanu, Daniela; Vernic, Raluca
2015
Discrete-time delay dynamics of boundedly rational monopoly. Zbl 1302.91135
Matsumoto, Akio; Szidarovszky, Ferenc
2014
One-dimensional maps with two discontinuity points and three linear branches: mathematical lessons for understanding the dynamics of financial markets. Zbl 1302.91199
Tramontana, Fabio; Westerhoff, Frank; Gardini, Laura
2014
Hedging and the competitive firm under correlated price and background risk. Zbl 1398.91664
Wong, Kit Pong
2014
Existence of financial equilibria with endogenous short selling restrictions and real assets. Zbl 1398.91390
Gori, Michele; Pireddu, Marina; Villanacci, Antonio
2014
Production and hedging in futures markets with multiple delivery specifications. Zbl 1398.91665
Wong, Kit Pong
2014
Numeraire portfolios and utility-based price systems under proportional transaction costs. Zbl 1398.91545
Sass, Jörn; Schäl, Manfred
2014
An application of nonparametric volatility estimators to option pricing. Zbl 1398.91602
Kenmoe, Romuald N.; Sanfelici, Simona
2014
Expectations and industry location: a discrete time dynamical analysis. Zbl 1310.91125
Agliari, Anna; Commendatore, Pasquale; Foroni, Ilaria; Kubin, Ingrid
2014
Selecting stochastic mortality models for the Italian population. Zbl 1398.91312
Biffi, Paola; Clemente, Gian Paolo
2014
The restricted convex risk measures in actuarial solvency. Zbl 1398.91335
Konstantinides, Dimitrios G.; Kountzakis, Christos E.
2014
A note on the existence of CAPM equilibria with homogeneous cumulative prospect theory preferences. Zbl 1398.91286
Del Vigna, Matteo
2014
Portfolio optimization for an investor with a benchmark. Zbl 1398.91530
Korn, R.; Lindberg, C.
2014
Optimal portfolio choice and consistent performance. Zbl 1398.91512
Chen, Xianzhe; Tian, Weidong
2014
Property rights for natural resources and sustainable growth in a two-country trade model. Zbl 1302.91161
Cabo, F.; Martín-Herrán, G.; Martínez-García, M. P.
2014
Relational consumption and nonlinear dynamics in an overlapping generations model. Zbl 1302.91136
Antoci, Angelo; Sodini, Mauro; Zarri, Luca
2014
Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes. Zbl 1302.91139
Gori, Luca; Sodini, Mauro
2014
Nonparametric correlation integral-based tests for linear and nonlinear stochastic processes. Zbl 1296.62220
Matilla-García, Mariano; Ruiz Marín, Manuel; Dore, Mohammed I.; Ojeda, Rina B.
2014
Pricing VIX options with stochastic volatility and random jumps. Zbl 1273.91442
Lian, Guang-Hua; Zhu, Song-Ping
2013
An optimal insurance design problem under Knightian uncertainty. Zbl 1277.91075
Bernard, Carole; Ji, Shaolin; Tian, Weidong
2013
The firm under uncertainty: real and financial decisions. Zbl 1274.91464
Broll, Udo; Wong, Kit Pong
2013
Optimal portfolio selection via conditional convex risk measures on $$L ^{p }$$. Zbl 1268.91160
Acciaio, Beatrice; Goldammer, Verena
2013
Multidimensional quasi-Monte Carlo Malliavin Greeks. Zbl 1345.91082
Cufaro Petroni, Nicola; Sabino, Piergiacomo
2013
Option-based risk management of a bond portfolio under regime switching interest rates. Zbl 1268.91174
Antonelli, Fabio; Ramponi, Alessandro; Scarlatti, Sergio
2013
Performance of investment strategies in the absence of correct beliefs. Zbl 1273.91416
Bektur, Çisem
2013
Portfolio optimization in a defaultable market under incomplete information. Zbl 1257.91039
Callegaro, Giorgia; Jeanblanc, Monique; Runggaldier, Wolfgang J.
2012
Risk aversion and risk vulnerability in the continuous and discrete case. Zbl 1257.91021
Bohner, Martin; Gelles, Gregory M.
2012
How should a convertible bond be decomposed? Zbl 1257.91048
Zhu, Song-Ping; Zhang, Jing
2012
On the linearity of the wage-profit relation in a Sraffa’s model: a mathematical summing-up. Zbl 1280.91123
Giorgi, G.; Zuccotti, C.
2012
Exchange rate bifurcation in a stochastic evolutionary finance model. Zbl 1264.91060
Gagnon, Gregory
2012
Optimal investment for executive stockholders with exponential utility. Zbl 1268.91163
Desmettre, Sascha
2012
...and 83 more Documents
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### Cited by 1,074 Authors

 11 D’Amico, Guglielmo 10 Manca, Raimondo 8 Maccheroni, Fabio 8 Marinacci, Massimo 7 Blot, Joël 7 Graziano, Maria Gabriella 7 Janssen, Jacques 6 Cretarola, Alessandra 6 Sabino, Piergiacomo 6 Tramontana, Fabio 5 Basile, Achille 5 Biancardi, Marta Elena 5 Cerreia-Vioglio, Simone 5 Figà-Talamanca, Gianna 5 Pesce, Marialaura 5 Rásonyi, Miklós 5 Sass, Jörn 5 Vigna, Elena 5 Villanacci, Antonio 5 Villani, Giovanni 5 Westerhoff, Frank H. 4 Assa, Hirbod 4 Campi, Luciano 4 Carassus, Laurence 4 Ceci, Claudia 4 Cheung, Ka Chun 4 Dana, Rose-Anne 4 Fabozzi, Frank J. 4 Faro, José Heleno 4 Gaudenzi, Marcellino 4 Jaber, Eduardo Abi 4 Li, Shenghong 4 Marazzina, Daniele 4 Matsumoto, Akio 4 Nagurney, Anna 4 Naimzada, Ahmad K. 4 Pascucci, Andrea 4 Polyrakis, Ioannis A. 4 Rachev, Svetlozar T. 4 Spizzichino, Fabio L. 4 Stoye, Jörg 4 Sushko, Iryna 4 Szidarovszky, Ferenc P. 4 Tian, Weidong 4 Wong, Hoi Ying 4 Wunderlich, Ralf 4 Yannelis, Nicholas Constantine 4 Zanette, Antonino 4 Zastawniak, Tomasz 3 Alcantud, José Carlos Rodríguez 3 Bade, Sophie 3 Bäuerle, Nicole 3 Bernard, Carole L. 3 Bo, Lijun 3 Bohner, Martin J. 3 Bordley, Robert F. 3 Burzoni, Matteo 3 Capponi, Agostino 3 Castagnoli, Erio 3 Chen, An 3 Colaneri, Katia 3 Cuchiero, Christa 3 Cufaro Petroni, Nicola 3 Daniele, Patrizia 3 de Castro, Luciano I. 3 De Donno, Marzia 3 Dominiak, Adam 3 Gerasímou, Georgios 3 Ghirardato, Paolo 3 Grant, Simon 3 Greco, Salvatore 3 Gu, Enguo 3 Haberman, Steven 3 Han, Bingyan 3 Hayek, Naïla 3 Heidarkhani, Shapour 3 Herzel, Stefano 3 Huynh, Van-Nam 3 Iannucci, Gianluca 3 Karni, Edi 3 Katsikis, Vasilios N. 3 Kelsey, David P. 3 Khan, Mohammed Ali 3 Klibanoff, Peter 3 Kountzakis, Christos E. 3 LiCalzi, Marco 3 Maggis, Marco 3 Martellotti, Anna 3 Martini, Claude 3 Menegatti, Mario 3 Mikkola, Kalle M. 3 Montrucchio, Luigi 3 Nakamori, Yoshiteru 3 Obloj, Jan K. 3 Olivieri, Annamaria 3 Ortobelli, Sergio 3 Parand, Kourosh 3 Pitacco, Ermanno 3 Platen, Eckhard 3 Rad, Jamal Amani ...and 974 more Authors
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 49 Decisions in Economics and Finance 47 Journal of Economic Theory 31 Journal of Mathematical Economics 30 Economic Theory 29 European Journal of Operational Research 23 International Journal of Theoretical and Applied Finance 21 Quantitative Finance 20 Insurance Mathematics & Economics 18 Finance and Stochastics 17 Theory and Decision 15 Mathematics and Financial Economics 14 Applied Mathematics and Computation 14 Mathematical Social Sciences 12 Journal of Economic Dynamics & Control 12 Mathematical Finance 12 SIAM Journal on Financial Mathematics 10 Economics Letters 9 Games and Economic Behavior 8 Annals of Operations Research 8 Applied Mathematical Finance 8 Methodology and Computing in Applied Probability 8 ASTIN Bulletin 7 Applied Mathematics and Optimization 7 Optimization 7 Mathematical Methods of Operations Research 6 Journal of Mathematical Analysis and Applications 6 Chaos, Solitons and Fractals 6 Journal of Optimization Theory and Applications 6 Computational Management Science 6 Journal of Industrial and Management Optimization 6 Annals of Finance 5 Advances in Applied Probability 5 Journal of Computational and Applied Mathematics 5 Mathematics of Operations Research 5 Stochastic Processes and their Applications 5 Communications in Nonlinear Science and Numerical Simulation 4 Fuzzy Sets and Systems 4 SIAM Journal on Control and Optimization 4 Journal of Economics 4 International Journal of Approximate Reasoning 4 Japan Journal of Industrial and Applied Mathematics 4 Computational Economics 4 Abstract and Applied Analysis 4 Scandinavian Actuarial Journal 4 North American Actuarial Journal 3 Mathematics and Computers in Simulation 3 Operations Research 3 Operations Research Letters 3 Stochastic Analysis and Applications 3 Social Choice and Welfare 3 The Annals of Applied Probability 3 Communications in Statistics. Theory and Methods 3 International Journal of Computer Mathematics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal of Difference Equations and Applications 3 Chaos 3 Probability in the Engineering and Informational Sciences 3 Fuzzy Optimization and Decision Making 3 Dynamic Games and Applications 3 Statistics & Risk Modeling 3 Nonautonomous Dynamical Systems 2 Computers & Mathematics with Applications 2 Physica A 2 Automatica 2 International Journal of Mathematics and Mathematical Sciences 2 International Journal of Game Theory 2 Journal of Applied Probability 2 Journal of Econometrics 2 Journal of Mathematical Psychology 2 Statistics & Probability Letters 2 Acta Applicandae Mathematicae 2 Econometric Reviews 2 Computational Statistics 2 Linear Algebra and its Applications 2 Mathematical Problems in Engineering 2 Positivity 2 Soft Computing 2 Review of Economic Design 2 Discrete and Continuous Dynamical Systems. Series B 2 Stochastics and Dynamics 2 Decision Analysis 2 Stochastic Systems 2 Minimax Theory and its Applications 1 The Canadian Journal of Statistics 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 Mathematical Biosciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Metrika 1 Theory of Probability and its Applications 1 Acta Mathematica Vietnamica 1 Information Sciences 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Journal of Multivariate Analysis 1 Journal of Philosophical Logic 1 Kybernetika 1 Mathematische Annalen 1 Numerical Functional Analysis and Optimization 1 Proceedings of the American Mathematical Society ...and 71 more Journals
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### Cited in 36 Fields

 618 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 184 Probability theory and stochastic processes (60-XX) 69 Operations research, mathematical programming (90-XX) 65 Statistics (62-XX) 59 Systems theory; control (93-XX) 42 Numerical analysis (65-XX) 37 Calculus of variations and optimal control; optimization (49-XX) 22 Partial differential equations (35-XX) 12 Ordinary differential equations (34-XX) 11 Dynamical systems and ergodic theory (37-XX) 9 Functional analysis (46-XX) 9 Computer science (68-XX) 8 Difference and functional equations (39-XX) 7 Measure and integration (28-XX) 6 Biology and other natural sciences (92-XX) 5 Mathematical logic and foundations (03-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 4 Operator theory (47-XX) 3 Real functions (26-XX) 3 Integral transforms, operational calculus (44-XX) 3 Integral equations (45-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Approximations and expansions (41-XX) 2 Convex and discrete geometry (52-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Mathematics education (97-XX)


text:
# Command-Line Options¶

The scenic command supports a variety of options. Run scenic -h for a full list with short descriptions; we elaborate on some of the most important options below.

## General Scenario Control¶

-m <model>, --model <model>

Specify the world model to use for the scenario, overriding any model statement in the scenario. The argument must be the fully-qualified name of a Scenic module found on your PYTHONPATH (it does not necessarily need to be built into Scenic).

-p <param> <value>, --param <param> <value>

Specify the value of a global parameter. This assignment overrides any param statements in the scenario. If the given value can be interpreted as an int or float, it is; otherwise it is kept as a string.

## Dynamic Simulations¶

-S, --simulate

Run dynamic simulations from scenes instead of plotting scene diagrams. This option will only work for scenarios which specify a simulator, which is done automatically by the world models for the simulator interfaces that support dynamic scenarios, e.g. scenic.simulators.carla.model and scenic.simulators.lgsvl.model. If your scenario is written for an abstract domain, like scenic.domains.driving, you will need to use the --model option to specify the specific model for the simulator you want to use.

--time <steps>

Maximum number of time steps to run each simulation (the default is infinity). Simulations may end earlier if termination criteria defined in the scenario are met.

--count <number>

Number of successful simulations to run (i.e., not counting rejected simulations). The default is to run forever.

## Debugging¶

-v <verbosity>, --verbosity <verbosity>

Set the verbosity level, from 0 to 3 (default 1):

0

Nothing is printed except error messages and warnings (to stderr). Warnings can be suppressed using the PYTHONWARNINGS environment variable.

1

The main steps of compilation and scene generation are indicated, with timing statistics.

2

Additionally, details on which modules are being compiled and the reasons for any scene/simulation rejections are printed.

3

Additionally, the actions taken by each agent at each time step of a dynamic simulation are printed.

format: plain


text:
# Phase velocity greater then the speed of light?

It is my understanding the the phase velocity of a wave can be greater then the speed of light. So imagine we had a wave packet consisting of a single sinusoidal wave; $$y=\sin(\omega t-kx)$$ Then from the definition of phase velocity, this wave will (if I am not mistaken) travel with the phase velocity, which as stated above can be greater then $c$. But in this case information is been passed greater then the speed of light, is it not? If we start the wave packet of at a point $A$ say and let it propagate to another point $B$ it will travel to $B$ faster than the speed of light and pass of the information of its frequency and wavelength. Why is this not breaking special relativity?

• As for matter wave, phase velocity has no physical significance, because the motion of the wave group, not the motion of the individual waves that make up the group, corr. to the motion of the body, & group velocity is less than $c$ as it should be. So , the matter wave doesn't violate special relativity. – user36790 Mar 7 '15 at 10:31
• Same is in the case for your concerned wave. +1 to Rennie's answer. – user36790 Mar 7 '15 at 10:34

The simple answer is that the wave packet travels at the group velocity not the phase velocity, and the group velocity is always less than or equal to $c$.
You might argue that you aren't using a wave packet. For example you might argue that you are just turning the light on and waiting for it to get to the point $B$. However any modulation of the wave intensity, including turning it on and off, will propagate at the group velocity.
• Hi, but this wave consists of many 'smaller waves' travelling with the phase velocity, does this not therefore mean that the front of the wave packet will reach $B$ at a time faster then the speed of light. – Quantum spaghettification Mar 7 '15 at 8:28
• @Joseph: yes, the packet does spread and therefore the leading edge moves faster than the average packet velocity. However the leading edge does not move at the phase velocity, it moves at a velocity $\le c$. – John Rennie Mar 7 '15 at 8:57


text: Seminar on Combinatorics 主講者: 李建平教授(雲南大學) 講題: Some Variants of Multiple Knapsack Problem 時間: 2012-02-17 (Fri.)  14:00 - 15:30 地點: 數學所 722 研討室 (台大院區) Abstract: Given m knapsacks with different capacities and a restricted bipartite graph G=(S∪T;E), where each vertex vi ?S∪T presents an item i with a size si and a profit pi, the two items i and j may be packed into same knapsack only when the two vertices vi and vj are adjacent in G, and for 1≦k≦m, the profit of each knapsack bk is defined as the total profit of the items packed into that knapsack bk. We consider two variants of the multiple knapsack problem with restricted bipartite graph in the following versions: (i) the objective is to maximize the total profit of items packed in m knapsacks (Max-Sum MKPB); (ii) the objective is to maximize the minimum profit of a knapsack among these m knapsacks (Max-Min MKPB). We obtain the following results: (1) two variants of the MKPB problem are NP-hard in a strong sense, and for any real number t > 0, the Max-Min MKPB problem cannot be approximated within a factor 1/2 + t; (2) we design two approximation algorithms to solve these two variants of the MKPB problem, respectively; (3) we finally present two optimal algorithms to solve them for the cases where all knapsacks have the same capacity, respectively. || Close window ||


text:
# desctable usage vignette

Desctable is a comprehensive descriptive and comparative tables generator for R.

Every person doing data analysis has to create tables for descriptive summaries of data (a.k.a. Table.1), or comparative tables.

Many packages, such as the aptly named tableone, address this issue. However, they often include hard-coded behaviors, have outputs not easily manipulable with standard R tools, or their syntax are out-of-style (e.g. the argument order makes them difficult to use with the pipe (%>%)).

Enter desctable, a package built with the following objectives in mind:

• generate descriptive and comparative statistics tables with nesting
• keep the syntax as simple as possible
• have good reasonable defaults
• be entirely customizable, using standard R tools and functions
• produce the simplest (as a data structure) output possible
• provide helpers for different outputs
• integrate with “modern” R usage, and the tidyverse set of tools

# Descriptive tables

## Simple usage

desctable uses and exports the pipe (%>%) operator (from packages magrittr and dplyr fame), though it is not mandatory to use it.

The single interface to the package is its eponymous desctable function.

When used on a data.frame, it returns a descriptive table:

iris %>%
desctable
##                         N        %     Mean        sd  Med IQR
## 1        Sepal.Length 150       NA       NA        NA 5.80 1.3
## 2         Sepal.Width 150       NA 3.057333 0.4358663 3.00 0.5
## 3        Petal.Length 150       NA       NA        NA 4.35 3.5
## 4         Petal.Width 150       NA       NA        NA 1.30 1.5
## 5             Species 150       NA       NA        NA   NA  NA
## 6     Species: setosa  50 33.33333       NA        NA   NA  NA
## 7 Species: versicolor  50 33.33333       NA        NA   NA  NA
## 8  Species: virginica  50 33.33333       NA        NA   NA  NA
desctable(mtcars)
##          N      Mean        sd     Med       IQR
## 1   mpg 32 20.090625 6.0269481  19.200   7.37500
## 2   cyl 32        NA        NA   6.000   4.00000
## 3  disp 32        NA        NA 196.300 205.17500
## 4    hp 32        NA        NA 123.000  83.50000
## 5  drat 32  3.596563 0.5346787   3.695   0.84000
## 6    wt 32        NA        NA   3.325   1.02875
## 7  qsec 32 17.848750 1.7869432  17.710   2.00750
## 8    vs 32        NA        NA   0.000   1.00000
## 9    am 32        NA        NA   0.000   1.00000
## 10 gear 32        NA        NA   4.000   1.00000
## 11 carb 32        NA        NA   2.000   2.00000

As you can see with these two examples, desctable describes every variable, with individual levels for factors. It picks statistical functions depending on the type and distribution of the variables in the data, and applies those statistical functions only on the relevant variables.

## Output

The object produced by desctable is in fact a list of data.frames, with a “desctable” class.
Methods for reduction to a simple dataframe (as.data.frame, automatically used for printing), conversion to markdown (pander), and interactive html output with DT (datatable) are provided:

iris %>%
desctable %>%
pander
N % Mean sd Med IQR
Sepal.Length 150 5.8 1.3
Sepal.Width 150 3.1 0.44 3 0.5
Petal.Length 150 4.3 3.5
Petal.Width 150 1.3 1.5
Species 150
setosa 50 33
versicolor 50 33
virginica 50 33
mtcars %>%
desctable %>%
datatable

You need to load these two packages first (and prior to desctable for DT) if you want to use them.

Calls to pander and datatable with “regular” dataframes will not be affected by the defaults used in the package, and you can modify these defaults for desctable objects.

Subsequent outputs in this vignette section will use DT. The datatable wrapper function for desctable objects comes with some default options and formatting such as freezing the row names and table header, export buttons, and rounding of values. Both pander and datatable wrapper take a digits argument to set the number of decimals to show. (pander uses the digits, justify and missing arguments of pandoc.table, whereas datatable calls prettyNum with the digits parameter, and removes NA values. You can set digits = NULL if you want the full table and format it yourself)

desctable chooses statistical functions for you using this algorithm:

• always show N
• if there are factors, show %
• if there are normally distributed variables, show Mean and SD
• if there are non-normally distributed variables, show Median and IQR

For each variable in the table, compute the relevant statistical functions in that list (non-applicable functions will safely return NA).

How does it work, and how can you adapt this behavior to your needs?

desctable takes an optional stats argument. This argument can either be:

• an automatic function to select appropriate statistical functions
• or a named list of
• statistical functions
• formulas describing conditions to use a statistical function.

### Automatic function

This is the default, using the stats_auto function provided in the package.

Several other “automatic statistical functions” are defined in this package: stats_auto, stats_default, stats_normal, stats_nonnormal.

You can also provide your own automatic function, which needs to

• accept a dataframe as its argument (whether to use this dataframe or not in the function is your choice), and
• return a named list of statistical functions to use, as defined in the subsequent paragraphs.
# Strictly equivalent to iris %>% desctable %>% datatable
iris %>%
desctable(stats = stats_auto) %>%
datatable

### Statistical functions

Statistical functions can be any function defined in R that you want to use, such as length or mean.

The only condition is that they return a single numerical value. One exception is when they return a vector of length 1 + nlevels(x) when applied to factors, as is needed for the percent function.

As mentioned above, they need to be used inside a named list, such as

mtcars %>%
desctable(stats = list("N" = length, "Mean" = mean, "SD" = sd)) %>%
datatable

The names will be used as column headers in the resulting table, and the functions will be applied safely on the variables (errors return NA, and for factors the function will be used on individual levels).

Several convenience functions are included in this package. For statistical function we have: percent, which prints percentages of levels in a factor, and IQR which re-implements stats::IQR but works better with NA values.

Be aware that all functions will be used on variables stripped of their NA values!
This is necessary for most statistical functions to be useful, and makes N (length) show only the number of observations in the dataset for each variable.

### Conditional formulas

The general form of these formulas is

predicate_function ~ stat_function_if_TRUE | stat_function_if_FALSE

A predicate function is any function returning either TRUE or FALSE when applied on a vector, such as is.factor, is.numeric, and is.logical.
desctable provides the is.normal function to test for normality (it is equivalent to length(na.omit(x)) > 30 & shapiro.test(x)$p.value > .1). The FALSE option can be omitted and NA will be produced if the condition in the predicate is not met. These statements can be nested using parentheses. For example: is.factor ~ percent | (is.normal ~ mean) will either use percent if the variable is a factor, or mean if and only if the variable is normally distributed. You can mix “bare” statistical functions and formulas in the list defining the statistics you want to use in your table. iris %>% desctable(stats = list("N" = length, "%/Mean" = is.factor ~ percent | (is.normal ~ mean), "Median" = is.normal ~ NA | median)) %>% datatable For reference, here is the body of the stats_auto function in the package: ## function (data) ## { ## shapiro <- data %>% Filter(f = is.numeric) %>% lapply(is.normal) %>% ## unlist ## if (length(shapiro) == 0) { ## normal <- F ## nonnormal <- F ## } ## else { ## normal <- any(shapiro) ## nonnormal <- any(!shapiro) ## } ## fact <- any(data %>% lapply(is.factor) %>% unlist) ## if (fact & normal & !nonnormal) ## stats_normal(data) ## else if (fact & !normal & nonnormal) ## stats_nonnormal(data) ## else if (fact & !normal & !nonnormal) ## list(N = length, % = percent) ## else if (!fact & normal & nonnormal) ## list(N = length, Mean = is.normal ~ mean, sd = is.normal ~ ## sd, Med = stats::median, IQR = is.factor ~ NA | IQR) ## else if (!fact & normal & !nonnormal) ## list(N = length, Mean = mean, sd = stats::sd) ## else if (!fact & !normal & nonnormal) ## list(N = length, Med = stats::median, IQR = IQR) ## else stats_default(data) ## } ## <bytecode: 0x56186ce05d90> ## <environment: namespace:desctable> ### Labels It is often the case that variable names are not “pretty” enough to be used as-is in a table. Although you could still edit the variable labels in the table afterwards using subsetting or string replacement functions, it is possible to mention a labels argument. The labels argument is a named character vector associating variable names and labels. You don’t need to provide labels for all the variables, and extra labels will be silently discarded. This allows you to define a “global” labels vector and use it for every table even after variable selections. mtlabels <- c(mpg = "Miles/(US) gallon", cyl = "Number of cylinders", disp = "Displacement (cu.in.)", hp = "Gross horsepower", drat = "Rear axle ratio", wt = "Weight (1000 lbs)", qsec = "¼ mile time", vs = "V/S", am = "Transmission", gear = "Number of forward gears", carb = "Number of carburetors") mtcars %>% dplyr::mutate(am = factor(am, labels = c("Automatic", "Manual"))) %>% desctable(labels = mtlabels) %>% datatable # Comparative tables ## Simple usage Creating a comparative table (between groups defined by a factor) using desctable is as easy as creating a descriptive table. It uses the well known group_by function from dplyr: iris %>% group_by(Species) %>% desctable -> iris_by_Species iris_by_Species ## Species: setosa (n=50) / N Species: setosa (n=50) / Mean ## 1 Sepal.Length 50 5.006 ## 2 Sepal.Width 50 3.428 ## 3 Petal.Length 50 NA ## 4 Petal.Width 50 NA ## Species: setosa (n=50) / sd Species: setosa (n=50) / Med ## 1 0.3524897 5.0 ## 2 0.3790644 3.4 ## 3 NA 1.5 ## 4 NA 0.2 ## Species: setosa (n=50) / IQR Species: versicolor (n=50) / N1 ## 1 0.400 50 ## 2 0.475 50 ## 3 0.175 50 ## 4 0.100 50 ## Species: versicolor (n=50) / Mean1 Species: versicolor (n=50) / sd1 ## 1 5.936 0.5161711 ## 2 2.770 0.3137983 ## 3 4.260 0.4699110 ## 4 NA NA ## Species: versicolor (n=50) / Med1 Species: versicolor (n=50) / IQR1 ## 1 5.90 0.700 ## 2 2.80 0.475 ## 3 4.35 0.600 ## 4 1.30 0.300 ## Species: virginica (n=50) / N2 Species: virginica (n=50) / Mean2 ## 1 50 6.588 ## 2 50 2.974 ## 3 50 5.552 ## 4 50 NA ## Species: virginica (n=50) / sd2 Species: virginica (n=50) / Med2 ## 1 0.6358796 6.50 ## 2 0.3224966 3.00 ## 3 0.5518947 5.55 ## 4 NA 2.00 ## Species: virginica (n=50) / IQR2 tests / p ## 1 0.675 1.505059e-28 ## 2 0.375 4.492017e-17 ## 3 0.775 4.803974e-29 ## 4 0.500 3.261796e-29 ## tests / test ## 1 . %>% oneway.test(var.equal = F) ## 2 . %>% oneway.test(var.equal = T) ## 3 kruskal.test ## 4 kruskal.test The result is a table containing a descriptive subtable for each level of the grouping factor (the statistical functions rules are applied to each subtable independently), with the statistical tests performed, and their p values. When displayed as a flat dataframe, the grouping header appears in each variable. You can also see the grouping headers by inspecting the resulting object, which is a deep list of dataframes, each dataframe named after the grouping factor and its levels (with sample size for each). str(iris_by_Species) ## List of 5 ##$ Variables                 :'data.frame':  4 obs. of  1 variable:
##   ..$Variables: chr [1:4] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" ##$ Species: setosa (n=50)    :'data.frame':  4 obs. of  5 variables:
##   ..$N : int [1:4] 50 50 50 50 ## ..$ Mean: num [1:4] 5.01 3.43 NA NA
##   ..$sd : num [1:4] 0.352 0.379 NA NA ## ..$ Med : num [1:4] 5 3.4 1.5 0.2
##   ..$IQR : num [1:4] 0.4 0.475 0.175 0.1 ##$ Species: versicolor (n=50):'data.frame':  4 obs. of  5 variables:
##   ..$N : int [1:4] 50 50 50 50 ## ..$ Mean: num [1:4] 5.94 2.77 4.26 NA
##   ..$sd : num [1:4] 0.516 0.314 0.47 NA ## ..$ Med : num [1:4] 5.9 2.8 4.35 1.3
##   ..$IQR : num [1:4] 0.7 0.475 0.6 0.3 ##$ Species: virginica (n=50) :'data.frame':  4 obs. of  5 variables:
##   ..$N : int [1:4] 50 50 50 50 ## ..$ Mean: num [1:4] 6.59 2.97 5.55 NA
##   ..$sd : num [1:4] 0.636 0.322 0.552 NA ## ..$ Med : num [1:4] 6.5 3 5.55 2
##   ..$IQR : num [1:4] 0.675 0.375 0.775 0.5 ##$ tests                     :'data.frame':  4 obs. of  2 variables:
##   ..$p : num [1:4] 1.51e-28 4.49e-17 4.80e-29 3.26e-29 ## ..$ test: chr [1:4] ". %>% oneway.test(var.equal = F)" ". %>% oneway.test(var.equal = T)" "kruskal.test" "kruskal.test"
##  - attr(*, "class")= chr "desctable"

You can specify groups based on any variable, not only factors:

# With pander output
mtcars %>%
group_by(cyl) %>%
desctable %>%
pander
cyl: 4 (n=11)
N

Med

IQR
cyl: 6 (n=7)
N1

Med1

IQR1
cyl: 8 (n=14)
N2

Med2

IQR2
tests
p

test
mpg 11 26 7.6 7 20 2.4 14 15 1.8 2.6e-06 kruskal.test
disp 11 108 42 7 168 36 14 350 88 1.6e-06 kruskal.test
hp 11 91 30 7 110 13 14 192 65 3.3e-06 kruskal.test
drat 11 4.1 0.35 7 3.9 0.56 14 3.1 0.15 0.00075 kruskal.test
wt 11 2.2 0.74 7 3.2 0.62 14 3.8 0.48 1.1e-05 kruskal.test
qsec 11 19 1.4 7 18 2.4 14 17 1.5 0.0062 kruskal.test
vs 11 1 0 7 1 1 14 0 0 3.2e-05 kruskal.test
am 11 1 0.5 7 0 1 14 0 0 0.014 kruskal.test
gear 11 4 0 7 4 0.5 14 3 0 0.0062 kruskal.test
carb 11 2 1 7 4 1.5 14 3.5 1.8 0.0017 kruskal.test

Also with conditions:

# With datatable output
iris %>%
group_by(Petal.Length > 5) %>%
desctable %>%
datatable

And even on multiple nested groups:

mtcars %>%
dplyr::mutate(am = factor(am, labels = c("Automatic", "Manual"))) %>%
group_by(vs, am, cyl) %>%
desctable %>%
datatable

In the case of nested groups (a.k.a. sub-group analysis), statistical tests are performed only between the groups of the deepest grouping level.

Statistical tests are automatically selected depending on the data and the grouping factor.

desctable choses the statistical tests using the following algorithm:

• if the variable is a factor, use fisher.test
• if the grouping factor has only one level, use the provided no.test (which does nothing)
• if the grouping factor has two levels
• and the variable presents homoskedasticity (p value for var.test > .1) and normality of distribution in both groups, use t.test(var.equal = T)
• and the variable does not present homoskedasticity (p value for var.test < .1) but normality of distribution in both groups, use t.test(var.equal = F)
• else use wilcox.test
• if the grouping factor has more than two levels
• and the variable presents homoskedasticity (p value for bartlett.test > .1) and normality of distribution in all groups, use oneway.test(var.equal = T)
• and the variable does not present homoskedasticity (p value for bartlett.test < .1) but normality of distribution in all groups, use oneway.test(var.equal = F)
• else use kruskal.test

But what if you want to pick a specific test for a specific variable, or change all the tests altogether?

desctable takes an optional tests argument. This argument can either be

• an automatic function to select appropriate statistical test functions
• or a named list of statistical test functions

### Automatic function

This is the default, using the tests_auto function provided in the package.

You can also provide your own automatic function, which needs to

• accept a variable and a grouping factor as its arguments, and
• return a single-term formula containing a statistical test function.

This function will be used on every variable and every grouping factor to determine the appropriate test.

# Strictly equivalent to iris %>% group_by(Species) %>% desctable %>% datatable
iris %>%
group_by(Species) %>%
desctable(tests = tests_auto) %>%
datatable

### List of statistical test functions

You can provide a named list of statistical functions, but here the mechanism is a bit different from the stats argument.

The list must contain either .auto or .default.

• .auto needs to be an automatic function, such as tests_auto. It will be used by default on all variables to select a test
• .default needs to be a single-term formula containing a statistical test function that will be used on all variables

You can also provide overrides to use specific tests for specific variables.
This is done using list items named as the variable and containing a single-term formula function.

iris %>%
group_by(Petal.Length > 5) %>%
desctable(tests = list(.auto   = tests_auto,
Species = ~chisq.test)) %>%
datatable

mtcars %>%
dplyr::mutate(am = factor(am, labels = c("Automatic", "Manual"))) %>%
group_by(am) %>%
desctable(tests = list(.default = ~wilcox.test,
mpg      = ~t.test)) %>%
datatable

You might wonder why the formula expression. That is needed to capture the test name, and to provide it in the resulting table.

As with statistical functions, any statistical test function defined in R can be used.

The conditions are that the function

• accepts a formula (variable ~ grouping_variable) as a first positional argument (as is the case with most tests, like t.test), and
• returns an object with a p.value element.

Several convenience function are provided: formula versions for chisq.test and fisher.test using generic S3 methods (thus the behavior of standard calls to chisq.test and fisher.test are not modified), and ANOVA, a partial application of oneway.test with parameter var.equal = T.

# Tips and tricks

In the stats argument, you can not only feed function names, but even arbitrary function definitions, functional sequences (a feature provided with the pipe (%>%)), or partial applications (with the purrr package):

mtcars %>%
desctable(stats = list("N"              = length,
"Sum of squares" = function(x) sum(x^2),
"Q1"             = . %>% quantile(prob = .25),
"Q3"             = purrr::partial(quantile, probs = .75))) %>%
datatable

In the tests arguments, you can also provide function definitions, functional sequences, and partial applications in the formulas:

iris %>%
group_by(Species) %>%
desctable(tests = list(.auto = tests_auto,
Sepal.Width = ~function(f) oneway.test(f, var.equal = F),
Petal.Length = ~. %>% oneway.test(var.equal = T),
Sepal.Length = ~purrr::partial(oneway.test, var.equal = T))) %>%
datatable

This allows you to modulate the behavior of desctable in every detail, such as using paired tests, or non htest tests.

# This is a contrived example, which would be better solved with a dedicated function
library(survival)

bladder$surv <- Surv(bladder$stop, bladder$event) bladder %>% group_by(rx) %>% desctable(tests = list(.default = ~wilcox.test, surv = ~. %>% survdiff %>% .$chisq %>% pchisq(1, lower.tail = F) %>% list(p.value = .))) %>%
datatable


text:
# Homework Help: Power physics homework

1. Jun 20, 2005

### Craig113

Hello people, pardon my poor grammar and my horrible spelling. Let my make it clear to all that in not looking for someone to do my homework. I just need a push on the right direction.
--------------------------------------------------------------------------

a ball with the mass of 50 grams hangs on a very light thread who has the lenght of 80 cm and swing back and forth (pendel). At the begining of the movement the maximum angle that the thread formed when moving was 35 degress, but after one minute tha angle had declined to 2o degress.The time for the ball to make one swing from its lowest point to its highest remained the same.

The question is: Is the power that the swinging energi (mekanic energi) from the pendel turns into other energi forms under one minute bigger or smaller than the averge power of the pendel?

Solution:

Well, i know how to calculate the power that turns the mekanic energi to other energiforms, its very easy. Power is P = delta E/ delta t
How much energi has the pendel lost under one minute? Tha answer to that question be found by comparing the highest level of potential energy for 35 and 20 degress. To do that you need to calculate how high the ball went from its lowest when de turning angle was 20 degress and 35 degress. That is easy to, just use basic trigonametry. When you have calculated the energ lost under one minute, get the power by using the formula P =E/60.

But as i understand it, the "average power" of the pendel is the energi amout
that turn from one form to another while the pendel swings one time from its highest point over ground to its lowest divided with the time it takes to preform the movement. To calculate this one must first calculate the speed of the pendel at the angles, divid the speed with 2, to get averege speed. ne must calculate the distance that the pendel travels by using the formula
(r*2 pi)/360 * 20 or 35. And calculate the time by dividing the distance with the average speed. When you have the time t you can calculate the power of the pendel for 20 and 35 degress. And finally calculate the "average power" of the pendel by adding the to powers for 29 and 35 degress and dividing them with two.
I have done all this, and my answer is that the average power of the pendel is much higher than the power that turns the pendels mekanic energi to other energiforms, why am i wrong? Its insane.

------------------

--------------------
A mousetrap is used as a engine for a small car with the mass of 50 gram.The car mus be able to travel 8 meters. the mousetraps arm is about 4 cm, and it can be pulled 180 degress. The force needed to pull the arm of the mousetrap is linear dependable to the turning angle. its at its lowest point 2 N and on its highest about 10 newton.

the question is: What it the maximum violocity this car can have?

Solution: The road that the "car" must travel is not of any importance.
the most important thing is to calculate how much energi can be feed into the spring of the mousetrap. You can get the violocity when you get the total energy by the formula E = 0.5 *mv^2. The distance/displacement you have to use a force F to "cock the spring" is given by a half circle, you get that by the formula 2*0.04*pi/2. The force you have to use depends of the angle. The energi used is A= F*s. Its in this case the same as the area of a
triangle with the hight 8 newton and the lenght of ( 2*0.04*pi/2). This calculation should give one the energi feed into the mousetrap spring?
And with the energi you can calculate the maximum speed.
am i wrong? Why then?

2. Jun 21, 2005

### Craig113

Why is nobody answering? Dont understand, have done something that against the rulez?

3. Jun 21, 2005

### whozum

The power lost due to friction is the change in PE at the peaks (or KE at the bottom) of each swing. I don't think thats what you were getting at above.

The average power of the pendulum would be the work done by the pendulum divided by the time period its done it in. Kind of ambiguous question if you ask me.

4. Jun 21, 2005

### geosonel

KE transferred to car = (1/2)mv2 = Energy from mousetrap = E

mousetrap force = F(θ) = (2 newtons) + { (8 newtons)*(θ/π) }
θ from 0 to π radians
F(θ) from 2 to 10 newtons

$$E \ = \ \int F \, ds \ = \ \int_{0}^{\pi} F \, r \cdot d\theta \ = \ \int_{0}^{\pi} \left ( 2 \, + \, 8 \frac {\theta}{\pi} \right ) \, (0.04) \cdot d\theta \ = \ \left [ (2)(0.04) \theta \, + \, (8)(0.04) \frac {\theta^2}{2 \pi} \right ]_{0}^{\pi}$$

$$E \ = \ (2)(0.04) \pi \ + \ \frac {(8)(0.04) \pi}{2} \qquad \mbox{ = energy stored in mousetrap and delivered to car}$$

complete calculations & calculate velocity

Last edited: Jun 21, 2005
5. Jun 22, 2005

### Craig113

---
Dear friend, i first thought that "The average power" ot the pendulum and the Power that turns the energi of the pendulum to other energy forms where two different powers. And yes, one can argue that they are. But in this problem the "average power" is meant the average power that turns the total energy of the pendulum to other energi forms. So the question is really: is the power that turns the enery of the pendulum to other enery form under one minute higher or lower than the power that turns the total energy of the pendulum to other energy forms? And the answer is:

the power that turns the pendels energy to other energy forms under one minute is higher.
The reason is that while the pendulum losses energy and speed, the ball of the pendulum travels less distance and is exposed to less friction and stopping power from the air, thus lossing less energy is lost after eatch swing to friction and air, and the pendulum losses less hight and speed, still the time of eatch swing is the same, that means less power. Thus the average power that turns the total energy of the pendulum to other energy forms is less than the same power under one minute. Meaning the lost of the pendulum energy to friction and air decline with every swing.

6. Jun 22, 2005

### Craig113

---
im dont get it. Its the right answer though.
This problem is at a level that dont require knowledge about integrals first of.
And second i dont understand this integral, you cant use 0 and pi as the integrals limits, why? because you dont use the force f to do the displacement o to pi. And how can the factor 8 be in integral? You dont cock the spring 8 meters do you?

7. Jun 22, 2005

### Craig113

---

I think i found a easier solution, but its still thanks to you.

The force needed for a displacement is as you earlier
said F = (2 + (8*(r/pi)), and the work and energy feeded in the
spring is A= (F*s), s can be calculated easily as its a half circle,
(0.04 * 2 * pi)/2= 0.12566....
To calculate the total work, we need an integral that uses the limit 0 to 0.12566.. and still can calculate the force needed to make the displacement with x as the displacement, but the formula F= (2 + (8*(r/pi)) uses the angel to do so. But it the angel is dependable to the displacement as follow

(s/0.12566) * pi = angle, from this we get the F= 2 + 8 * ((s/0,12566)*pi)/pi
or put more simple F= 2 + 8* (s/0,12566..), this formula can be used in one integral with the lower limit 0 and the upper 0,12566. and you get the full energi of the spring.

8. Jun 22, 2005

good work!


text:
SHOGUN  4.1.0
RationalApproximationIndividualJob.h File Reference

Go to the source code of this file.

## Classes

singleton  SGVector< T >
shogun vector More...

singleton  CLinearOperator< T >
Abstract template base class that represents a linear operator, e.g. a matrix. More...

singleton  CLinearSolver< T, ST >
Abstract template base class that provides an abstract solve method for linear systems, that takes a linear operator $$A$$, a vector $$b$$, solves the system $$Ax=b$$ and returns the vector $$x$$. More...

class  CRationalApproximationIndividualJob
Implementation of independent job that solves one of the family of shifted systems in rational approximation of linear operator function times a vector using a direct linear solver. The shift is moved inside the operator. compute calls submit_results of the aggregator with CVectorResult which is the solution vector for that shift multiplied by complex weight (See CRationalApproximation) More...

SHOGUN Machine Learning Toolbox - Documentation


text:
Building blocks

Triangles solution

Here are three triangles with some side lengths and angles marked. Express the missing side lengths in terms of $\sin \theta$, $\cos \theta$ and $\tan \theta.$

• How can using side length ratios for $\sin \theta$, $\cos \theta$ and $\tan \theta$ help you?

From side $EF$ we have $\tan \theta = \dfrac{\sin \theta}{\cos \theta}.$
We can start by relabelling the triangles’ sides using $\sec \theta$, $\cosec \theta$ and $\cot \theta.$
Using Pythagoras’ theorem for each triangle gives us three results relating pairs of functions $\cos^2 \theta + \sin^2 \theta = 1 \quad \cot^2 \theta + 1 = \cosec^2 \theta \quad \text{and} \quad 1 + \tan^2 \theta = \sec^2 \theta.$


text:
# Equilibrium Points of DE

1. Oct 27, 2013

### FeDeX_LaTeX

The problem statement, all variables and given/known data
Find the equilibrium points of the system, determine their type and sketch the phase portrait.

$\frac{dx}{dt} = -3y + xy - 10, \frac{dy}{dt} = y^2 - x^2$

The attempt at a solution

Putting it together:

$\frac{dy}{dx} = \frac{y^2 - x^2}{-3y + xy - 10} \equiv \frac{Q(x,y)}{P(x,y)}$

Here, we see that the horizontal nullclines are plotted along the line $y = \pm x$ and the vertical nullclines along the curve $y = \frac{10}{x - 3}$.

We form the Jacobian, i.e.

J = $\left( \begin{array}{cc} P_x & P_y \\ Q_x & Q_y \end{array} \right)$ = $\left( \begin{array}{cc} y & x - 3 \\ -2x & -2y \end{array} \right)$

So $-tr(J) = y$ and $det(J) = 2x^2 - 2y^2 - 3$.

My question is, where do I go from here? Through using a differential equation plotter, I can see that the equilibrium points are a spiral source and spiral sink at (5,5) and (-2,-2) respectively. How does one deduce this from the Jacobian?

2. Oct 27, 2013

### FeDeX_LaTeX

Never mind, I've overcomplicated it -- all I needed to do was solve that system of DEs for x and y (substituting x = y).

The magic of the Homework board strikes again!


text:
# Show that a group is isomorphic to $\Bbb R$

$\def\R{\mathbb R}$Let $$G = \mathrm{Aff}(\R) := \{ f\colon\R\to\R\mid f \colon x\mapsto ax+b, a \in \R^*, b \in \R \}$$ Then $(G,\circ)$ is a group where $\circ$ denotes function composition $(f \circ g)(x) = f(g(x))$. Now let $$N := \{ f\in G\mid f\colon x\mapsto x+d, d \in \R \}$$ and $$H := \{ g\in G \mid x \mapsto cx, c \in \R^*\}$$ I have shown that $G$ is a group and that $N$ and $H$ are subgroups of $G$. Now I have to show that $N$ is isomorphic to $\R$ and that $H$ is isomorphic to $\R^*$. After that I have to show that $G$ is the semidirect product of $N$ by $H$.

I am stuck at showing that they are isomorphic. Help is appreciated. Thanks

-
The bijections are implicitly given when the sets $N,H$ were given by formulas: each $f\in N$ corresponds to its determining parameter $d\in\Bbb R$, and each $g\in H$ corresponds to its parameter $c\in\Bbb R^*$. The only thing to prove is that they preserve the given group operation, $+$ in case of $N$ and $\cdot$ in case of $H$. –  Berci Nov 23 '12 at 12:07

At first try to show that $G\simeq N \rtimes H$. I think that's easy to show. This is not requested but I do believe it's a good exercise.

Now my hint. To do what you want demonstrate that: $\forall \tau_d \in N$ such that $\tau_d(x)= x+d$, $\varphi: N \rightarrow \mathbb{R}$ such that $\varphi(\tau_d)= d$ is an isomorphism. "Same" thing try to do for $H$.

In this sense $G\simeq \mathbb{R}\rtimes \mathbb{R}^{*}$.

-
ok so i have shown that φ(τd) is an isomorphism for both N and H. Only thing left now is to show that G is a semidirect product of N and H, G≃N⋊H. –  grendizer Nov 26 '12 at 11:24
If you want an idea consider: $\chi: N \rtimes H \rightarrow G$ such that $\chi((a,b))=\tau_{a,b}$, considering that $\tau$ such that $\tau(x)=ax+b$. –  Ivan Nov 26 '12 at 23:22
thanks! got it all done. –  grendizer Nov 29 '12 at 9:38
You're welcome! –  Ivan Nov 29 '12 at 10:54

Well, let's look at the mapping $\theta\colon \mathbb{R} \to N$ defined like this: for every $d \in \mathbb{R}$ set $\theta(d) = f$, where $f\colon \mathbb{R} \to \mathbb{R},\ f(x) = x + d \quad \forall x \in \mathbb{R}$. In human words, $\theta$ maps each $d \in \mathbb{R}$ to the function that "shifts" all numbers by $d$.

Can you prove that $\theta$ is a homomorphism from $\mathbb{R}$ to $N$? That it is an isomorphism?

-


text:
# Understanding non-equivalence of proof lengths according to proof systems

Here, in section 4.3, Fortnow says:

But to prove P != NP we would need to show that tautologies
cannot have short proofs in an arbitrary proof system.

I am trying to understand the logic leading to this conclusion. Do I get it right when I say:

1. Haken showed that under a Frege proof system, solving the pigeonhole principle for $$m=n+1$$ is intractable.
2. However, with an extended Frege a proof system based on cutting planes, solving the pigeonhole principle for $$m=n+1$$ is always achievable in polynomial time.
3. Therefore, if one proves intractability of say k-SAT in a proof system, it does not imply that solving k-SAT would be intractable in another proof system.

Is that right? Else, what am I missing?

• Haken's result is for Resolution, which is weaker than Frege. Similar results exist for bounded-depth Frege. But no such lower bounds are known for general Frege. Nov 11 '19 at 16:59
• I think that the argument you're looking for is this: There is a proof system under which all proofs for a tautology are polynomial iff NP = co-NP because you'd have short certificate for co-NP problems. Nov 12 '19 at 9:35
• I believe everything you said is correct. I note that your point #3 could hold regardless of points #1 and #2 - points #1 and #2 are just a concrete example of where this has provably happened. Nov 17 '19 at 5:20
• @Joshua, you should make your last comment an answer. Many thanks. Nov 19 '19 at 13:57
• A comment on your points 1 & 2: Extended Frege Systems (EF) are not based on Cutting Planes. They are two different proof systems that both have short proofs of the pigeonhole principle (PHP). In fact, EF and even just Frege systems simulate Cutting Planes, so - contrary to your claim in #1 - Frege systems have short proofs of PHP. Lower bounds for PHP are only known for Resolution (and some algebraic proof systems), as Joshua already said. Nov 20 '19 at 8:18


text:
# Net Force on a circular current carrying wire, from an infinite wire.

1. Apr 26, 2014

1. The problem statement, all variables and given/known data

-I've attached a picture of the problem-

An inﬁnitely long straight wire of steady current I1 is placed to the left of a circular wire of current I2 and radius a as shown. The center of the circular wire is distance d(≥ a) away from the straight wire. Let’s ﬁnd the net magnetic (Lorentz) force acting on the entire circular wire as follows:

(A) Express the magnetic ﬁeld Bp at point P (due to the
current I1) in given quantities (including its direction).

(B) The Lorentz force due to the magnetic ﬁeld Bp acting on a small current segment I2dℓ at P is given by

dF = I2dℓ × Bp

Express dF = (dFx, dFy, dFz) in component representation in given quantities.

(C) By integrating your results from (B) show explicitly that the net Lorentz force for the
entire circular wire is given by

Fnet = µoI1I2$\left(1-[itex]\frac{d}{\sqrt{d2-a2}}$\right)$[itex]\hat{y}$

2. Relevant equations

Most given in question.

Bp=$\frac{-μ0I1}{2π(d+x)}$

3. The attempt at a solution

The first two parts I got through pretty easily. Part (A) was just giving the equation of the B-field for an infinite wire. For part (B) I ended up with:

dF=$\left(\frac{-μ0I1I2acosødø}{2(d+acosø)}\right)$$\hat{x}$+$\left(\frac{-μ0I1I2asinødø}{2(d+acosø)}\right)$$\hat{y}$

which I got from taking the cross product of I2dl and Bp, and am fairly certain is correct.

Now, for part (C) I keep getting stuck, I see what I'm supposed to get for Fnet, but my answer always has a natural log, or becomes zero, and I don't know how else to approach the problem.

#### Attached Files:

• ###### Prob6Pic.jpg
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2. Apr 26, 2014

### TSny

Yes, I think that's correct. (I tried to fix the latex, hope I got it the way you intended.)

The integration of the y-component is straightforward. (The answer for this component should also be evident by symmetry.) The x-integration seems more difficult. I threw it into Mathematica and it popped out the answer. I also managed to do it by converting it to a contour integral in the complex plane. I'm not seeing an elementary way to do it, but I'm probably just not seeing it. I spent a few minutes searching integral tables on the internet but did not find it.

The answer for the net force that you stated in part (C) appears to have the wrong direction.

3. Apr 26, 2014


text:
Strange compilation errors with mingw

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I've recently been getting too many INTERNAL COMPILER ERRORs with VC++ for my patience and so decided to try to switch to using mingw instead of the compiler that comes with VC++ (tried this before... but I finally found a descent alternative IDE as well). The problem that I get compiling my sources seems quite strange, I have the function:
inline v2 norm()
{
float l = length();
>>>	return v2(x/l,y/l);

}

The line with the carrots (>>>) generates the error: error: no matching function for call to 'v2::v2(v2)' I have the constructors:
	inline v2(float ix,float iy){x=ix;y=iy;}
inline v2(float *v){memcpy(&x,v,sizeof(float)*2);}
inline v2(v2 &o){x=o.x;y=o.y;}

And this sort of thing always compiled with VC++ (of course it's not exactly standards compliant), so could someone point out my stupid mistake here? I've tried playing around with it for a while to no avail, and all help is greatly appreciated, ~SPH

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Maybe not answering your real question: about the Internal compiler errors: are you compiling source that you have one a network drive? Visual C++ seems unable to handle that, copy it to a local drive and your fine..

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I think the gcc compiler wants a constructor of the form:
inline v2(const v2& o) { ... }

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you want:
inline v2(const v2 &o){x=o.x;y=o.y;}

edit: beaten by 30seconds :p

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Your copy constructor should take a reference-to-const:
inline v2(v2 const & o);

Enigma

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>> Message put in its own thread <<<

[Edited by - ShmeeBegek on June 23, 2005 11:41:42 AM]

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typename list<Character*>::iterator it;

iterator is a dependent name and therefore requires the typename keyword to disambiguate it.

Enigma

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# Seminar

We typically have seminars on Wednesday at noon in Malone 228.  All seminar announcements will be sent to the theory mailing list.

Jul
2
Mon
[Theory Seminar] Sai Lakshmi Bhavana Obbattu
Jul 2 @ 12:00 pm – 1:00 pm

Speaker: Sai Lakshmi Bhavana Obbattu
Affiliation: IISC Bangalore, India

Title: Privacy Amplification from Non-malleable Codes

The goal of a Privacy Amplification (PA) protocol is to allow two parties, who start out sharing a non-uniform secret ‘w’, to agree on a uniform secret ‘k’, in the presence of a computationally unbounded man-in-the-middle adversary. An interactive PA protocol is rated based on three parameters: 1) Number of rounds, 2) Entropy loss (entropy of w – |k|), and 3) Min-entropy requirement for w, while the asymptotically optimal parameters are 2, O(s) and O(s+log n) respectively (where s is the security parameter and n =|w|). There have been two popular approaches to solve this problem: one using use bit authentication protocols and the other using non-malleable extractors, but none of the prior protocols using these approaches had all asymptotically optimal parameters.

We give an alternate approach to solve the problem using Non-malleable Codes (NMCs). This approach results in a 8-round protocol with min-entropy requirement O(s+log n) and an entropy loss of O(s log s). Augmented NMCs with better parameters would result in optimal entropy loss of O(s). Our result is one of the first information theoretic applications of NMCs. In this talk, I will introduce NMCs and show connection of NMCs to PA.

In a concurrent and independent work, Xin Li gives a protocol with asymptotically optimal parameters based on non-malleable extractors. Because all known approaches have large hidden constants, exploring alternatives is necessary if we hope to get practical concrete parameters

The talk is based on:

Eshan Chattopadhyay, Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu and Sruthi Sekar. Privacy Amplification from Non-malleable Codes. (eprint.iacr.org/2018/293)

Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu and Sruthi Sekar. Non-malleable Randomness Encoders and their Applications (Eurocrypt 2018)

Bio: Sai Lakshmi Bhavana Obbattu is a doctoral student at Indian Institute of Science(IISc), Bangalore, advised by Dr. Bhavana Kanukurthi. Her publication venues include the Theory of Cryptography Conference (TCC) and Eurocrypt. Her TCC publication on Four-state Non-malleable Codes was invited to the Journal of Cryptology. She received her Integrated Dual Degree (B.Tech and M.Tech) from IIT(BHU), Varanasi. Her research interests include Non-malleable codes, Privacy Amplification and Applied Multi-party computation.

Aug
23
Thu
[Theory Seminar] Akash Kumar @ Malone 338
Aug 23 @ 12:00 pm – 1:00 pm

Speaker: Akash Kumar
Affiliation: Purdue University
Location: Malone 338 (note change of location)

Title:
Finding Minors in Sublinear time in Bounded degree graphs with (almost) optimal one-sided query complexity.

Abstract:
Let G be an undirected, bounded degree graph with n vertices. Fix a finite graph H, and suppose one must remove \varepsilon n edges from G to make it H-minor free (for some small constant \varepsilon > 0). We give an n^{1/2+o(1)}-time randomized procedure that, with high probability, finds an H-minor in such a graph. For an example application, suppose one must remove \varepsilon n edges from a bounded degree graph G to make it planar. This result implies an algorithm, with the same running time, that produces a K_{3,3} or K_5 minor in G. No sublinear time bound was known for this problem, prior to this result.

By the graph minor theorem, we get an analogous result for any minor-closed property. Up to n^{o(1)} factors, this resolves a conjecture of Benjamini-Schramm-Shapira (STOC 2008) on the existence of one-sided property testers for minor-closed properties. Furthermore, our algorithm is nearly optimal, by an \Omega(\sqrt{n}) lower bound of Czumaj et al (RSA 2014).

Prior to this work, the only graphs H for which non-trivial property testers were known for H-minor freeness are the following: H being a forest or a cycle (Czumaj et al, RSA 2014), K_{2,k}, (k\times 2)-grid, and the k-circus (Fichtenberger et al, Arxiv 2017).

(Joint work with C. Seshadhri and Andrew Stolman).

Sep
5
Wed
[Theory Seminar] Welcome and Introductions
Sep 5 @ 12:00 pm – 1:00 pm

Welcome and Introductions

Sep
12
Wed
[Theory Seminar] Zhengzhong Jin
Sep 12 @ 12:00 pm – 1:00 pm

Speaker: Zhengzhong Jin
Affiliation: JHU

Title: Deterministic Document Exchange Protocols, and Almost Optimal Binary Codes for Edit Errors

Abstract:
We study two basic problems regarding edit error, i.e. document exchange and error correcting codes for edit errors (insdel codes). For message length n and edit error upper bound k, it is known that in both problems the optimal sketch size or the optimal number of redundant bits is Θ(k log n/k). However, known constructions are far from achieving these bounds.

We significantly improve previous results on both problems. For document exchange, we give an efficient deterministic protocol with sketch size O(k log^2 n/k). This significantly improves the previous best known deterministic protocol, which has sketch size O(k^2+k log^2 n). For binary insdel codes, we obtain the following results:

1. An explicit binary insdel code which encodes an n-bit message x against k errors with redundancy O(k log^2 n/k). In particular this implies an explicit family of binary insdel codes that can correct ε fraction of insertions and deletions with rate 1−O(ε log^2(1/ε))=1−\tilde {O}(ε).

2. An explicit binary insdel code which encodes an n-bit message x against k errors with redundancy O(k log n). This is the first explicit construction of binary insdel codes that has optimal redundancy for a wide range of error parameters k, and this brings our understanding of binary insdel codes much closer to that of standard binary error correcting codes.

In obtaining our results we introduce the notion of ε-self matching hash functions and ε-synchronization hash functions. We believe our techniques can have further applications in the literature.

Oct
3
Wed
[Theory Seminar] Marius Zimand
Oct 3 @ 12:00 pm – 1:00 pm

Speaker: Marius Zimand
Affiliation: Towson University

Title: An operational characterization of mutual information in algorithmic information theory

Abstract: An operational interpretation of the concept of mutual information in the framework of Kolmogorov complexity has been elusive till now. We show that the mutual information of any pair of strings x and y is equal, up to logarithmic precision, to the length of the longest shared secret key that two parties, one having x and the complexity profile of the pair and the other one having y and the complexity profile of the pair, can establish via a probabilistic protocol with interaction on a public channel. We establish the communication complexity of secret key agreement protocols that produce a secret key of maximal length, for protocols with public randomness. We show that if the communication complexity drops below the established threshold then only very short secret keys can be obtained.

This is joint work with Andrei Romashchenko.

Oct
10
Wed
[Theory Seminar] Yasamin Nazari
Oct 10 @ 12:00 pm – 1:00 pm

Speaker: Yasamin Nazari
Affiliation: JHU

Title: Distributed Distance-Bounded Network Design Through Distributed Convex Programming

Abstract:
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner, this is essentially the only class of linear programs for which such an algorithm is known. In this work we provide a distributed algorithm for solving a different class of convex programs which we call “distance-bounded network design convex programs”. These can be thought of as relaxations of network design problems in which the connectivity requirement includes a distance constraint (most notably, graph spanners). Our algorithm runs in O((D/ϵ)logn) rounds in the LOCAL model and finds a (1+ϵ)-approximation to the optimal LP solution for any 0<ϵ≤1, where D is the largest distance constraint. While solving linear programs in a distributed setting is interesting in its own right, this class of convex programs is particularly important because solving them is often a crucial step when designing approximation algorithms. Hence we almost immediately obtain new and improved distributed approximation algorithms for a variety of network design problems, including Basic 3- and 4-Spanner, Directed k-Spanner, Lowest Degree k-Spanner, and Shallow-Light Steiner Network Design with a spanning demand graph. Our algorithms do not require any "heavy" computation and essentially match the best-known centralized approximation algorithms, while previous approaches which do not use heavy computation give approximations which are worse than the best-known centralized bounds.

Oct
17
Wed
[Theory Seminar] Karthik Abinav Sankararaman @ Malone 228
Oct 17 @ 12:00 pm – 1:00 pm

Speaker: Karthik Abinav Sankararaman
Affiliation: University of Maryland

Title: Adversarial Bandits with Knapsacks

Abstract: In this talk we will discuss the multi-armed bandits problem with resource constraints under the adversarial setting. In this problem, we have an interactive and repeated game between the algorithm and an adversary. Given T time-steps, d resources, m actions and budgets B1, B2, .. Bd, the algorithm chooses one of the m actions at each time-step. An adversary then reveals a reward and consumption for each of the d resources corresponding to this action. The time-step at which the algorithm runs out of the d resources (i.e., the total consumption for resource j > Bj), the game stops and the total reward is the sum of rewards obtained until the stopping time. The goal is to maximize the competitive ratio; the ratio of the total reward of the algorithm to the expected reward of a fixed distribution that knows all the rewards and consumption ahead of time. We give an algorithm for this problem whose competitive ratio is tight (matches the lower-bound). Moreover the algorithmic tools extends in an (almost) black-box fashion to also give an algorithm for the stochastic setting thus giving a “best-of-both-worlds” algorithm where the algorithm need not know a-priori if the input is adversarial or i.i.d. Finally we conclude with applications and special cases including the Dynamic Pricing problem.

This talk is based on a recent working paper with Nicole Immorlica, Rob Schapire and Alex Slivkins.

Oct
24
Wed
[Theory Seminar] Nithin Varma
Oct 24 @ 12:00 pm – 1:00 pm

Speaker: Nithin Varma
Affiliation: Boston University

Title: Separating erasures and errors in property testing using local list decoding

Abstract:
Corruption in data can be in the form of erasures (missing data) or errors (wrong data). Erasure-resilient property testing (Dixit, Raskhodnikova, Thakurta, Varma ’16) and tolerant property testing (Parnas, Ron, Rubinfeld ’06) are two formal models of sublinear algorithms that account for the presence of erasures and errors in input data, respectively.

We first show that there exists a property P that has an erasure-resilient tester whose query complexity is independent of the input size n, whereas every tolerant tester for P has query complexity that depends on n. We obtain this result by designing a local list decoder for the Hadamard code that works in the presence of erasures, thereby proving an analog of the famous Goldreich-Levin Theorem. We also show a strengthened separation by proving that there exists another property R such that R has a constant-query erasure-resilient tester, whereas every tolerant tester for R requires n^{Omega(1)} queries. The main tool used in proving the strengthened separation is an approximate variant of a locally list decodable code that works against erasures.

Joint work with Sofya Raskhodnikova and Noga Ron-Zewi.

Nov
7
Wed
[Theory Seminar] Jalaj Upadhyay
Nov 7 @ 12:00 pm – 1:00 pm

Affiliation: JHU

Title: Differentially Private Spectral Sparsification of Graphs
Abstract:
In this talk, we will discuss differentially private spectral sparsification of graphs. We argue that traditional spectral sparsification where the output graph is a subgraph of the input graph is not possible with differential privacy. This motivates us to define a relaxed version of spectral sparsification of graphs.

We consider edge-level privacy, i.e., neighboring graphs differs in one edge with weight one. We give efficient $(\alpha,\beta)$-differentially private algorithms that, on input a dense graph G, construct a spectral sparsification of G. Our output graphs has $O(n/\eps^2)$ weighted edges, which matches the best known non-private algorithms.

We can use our private sparse graph to solve various combinatorial and learning problems on graphs efficiently while preserving differential privacy. Some examples include all possible cut queries, Max-Cut, Sparse-Cut, Edge-Expansion, Laplacian eigenmaps, etc.

This talk is based on a joint work with Raman Arora and Vladimir Braverman.

Nov
16
Fri
Capital Area Theory Day @ Georgetown University
Nov 16 all-day


text:
A Fokker-Planck model of Dense Rotating Stellar Clusters
Session 104 -- Globilar Clusters
Display presentation, Thursday, 12, 1995, 9:20am - 6:30pm

## [104.16] A Fokker-Planck model of Dense Rotating Stellar Clusters

J.Girash (CfA)

We are in the process of building a computational machine to model dense stellar clusters, as at the centres of galaxies, using the orbit-averaged Fokker-Planck equation in two-dimensional action-angle space. The model expands the work of Quinlan \& Shapiro (1990 ApJ 356, 483) to include rotation and associated effects: ellipticity and angular momentum. A non-axisymmetric component of the potential (i.e. the formation of a stellar bar) is invoked to increase the efficiency of angular momentum transport. Following Q\&S we plan to include of order 10 distribution functions, each representing a stellar population a factor of two more massive than the next; in addition there will be a separate, non-collisional bar-star distribution function; the other stars will interact with the bulk potential of these bar stars. The goal is to verify that angular momentum can be removed from the core of the cluster quickly enough so that the constraint of rotational support no longer prevents the formation of a massive \$\sim1000M_\odot\$ object at the centre. This would be the seed black hole for the formation of an active galactic nucleus.